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Measurement Expressions
Advanced Design System 2011
September 2011
Measurement Expressions
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Measurement Expressions
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Measurement Expressions
Introduction to Measurement Expressions . . . . . . . . . . . . . . . .
Using Measurement Expressions in Advanced Design System . .
Circuit Budget Functions . . . . . . . . . . . . . . . . . . . . . . . . . . .
Circuit Envelope Functions . . . . . . . . . . . . . . . . . . . . . . . . .
Data Access Functions for Measurement Expressions . . . . . . .
FrontPanel Eye Diagram Functions . . . . . . . . . . . . . . . . . . . .
FrontPanel S-Parameter TDR Functions . . . . . . . . . . . . . . . .
Harmonic Balance Functions For Measurement Expressions . .
Jitter Analysis Functions . . . . . . . . . . . . . . . . . . . . . . . . . . .
Math Functions For Measurement Expressions . . . . . . . . . . .
Signal Processing Functions . . . . . . . . . . . . . . . . . . . . . . . .
S-Parameter Analysis Functions for Measurement Expressions
Statistical Analysis Functions . . . . . . . . . . . . . . . . . . . . . . .
Transient Analysis Functions . . . . . . . . . . . . . . . . . . . . . . . .
Utility Functions for Measurement Expressions . . . . . . . . . . .
Duplicated Expression Names . . . . . . . . . . . . . . . . . . . . . . . .
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350
Measurement Expressions
Introduction to Measurement
Expressions
This document describes the measurement expressions that are available for use with
several Agilent EEsof EDA products. For a complete list of available measurement
functions, refer to the Measurement Expression Functions (by category) (expmeas).
Measurement expressions are equations that are evaluated during simulation post
processing. They can be entered into the program using various methods, depending on
which product you are using. Unlike the expressions described in Simulator Expressions
(expsim), these expressions are evaluated after a simulation has completed, not before
the simulation is run. Measurement expressions can also be easily used in a Data Display.
For more information on entering equations in a data display, refer to Data Display (data).
Although there is some overlap among many of the more commonly used functions,
measurement expressions and simulator expressions are derived from separate sources,
evaluated at different times, and can have subtle differences in their usages. Thus, these
two types of expressions need to be considered separately. For an overview of how
measurement expressions are evaluated, refer to How Measurement Expressions are
Evaluated.
How Measurement Expressions are Evaluated
Within this document you will find information on:
Measurement Expressions Syntax
7
Measurement Expressions
Manipulating Simulation Data with Expressions
Information on working with different types of data.
Information specific to entering simulator expressions in your particular product.
You will also find a complete list of functions that can be used as measurement
expressions individually, or combined together as a nested expression. These functions
have been separated into libraries and are listed in alphabetical order within each library.
The functions available include:
Circuit Budget Functions (expmeas)
Circuit Envelope Functions (expmeas)
Data Access Functions (expmeas)
Harmonic Balance Functions (expmeas)
Math Functions (expmeas)
Signal Processing Functions (expmeas)
S-Parameter Analysis Functions (expmeas)
Statistical Analysis Functions (expmeas)
Transient Analysis Functions (expmeas)
For a complete list of all functions provided in this document, refer to the Table of
Contents (expmeas).
Measurement Expressions Syntax
Use the following guidelines when creating measurement expressions:
Measurement expressions are based on the mathematical syntax in Application
Extension Language (AEL).
Function names, variable names, and constant names are all case sensitive in
measurement expressions.
Use commas to separate arguments.
White space between arguments is acceptable.
Case Sensitivity
All variable names, functions names, and equation names are case sensitive in
measurement expressions.
8
Measurement Expressions
Variable Names
Variables produced by the simulator can be referenced in equations with various degrees
of rigidity. In general a variable is defined as:
DatasetName.AnalysisName.AnalysisType.CircuitPath.VariableName
By default, in the Data Display window, a variable is commonly referenced as:
DatasetName..VariableName where the double dot ".." indicates that the variable is
unique in this dataset. If a variable is referenced without a dataset name, then it is
assumed to be in the current default dataset.
When the results of several analyses are in a dataset, it becomes necessary to specify the
analysis name with the variable name. The double dot can always be used to pad a
variable name instead of specifying the complete name.
In most cases a dataset contains results from a single analysis only, and so the variable
name alone is sufficient. The most common use of the double dot is when it is desired to
tie a variable to a dataset other than the default dataset.
Built-in Constants
Constant Description
Value
PI (also
pi)
3.1415926535898
e
Euler's constant
2.718281822
ln10
natural log of 10
2.302585093
boltzmann Boltzmann's constant
1.380658e-23 J/K
qelectron
electron charge
1.60217733e-19 C
planck
Planck's constant
6.6260755e-34 J*s
c0
Speed of light in free
space
2.99792e+08 m/s
e0
Permittivity of free space
8.85419e-12 F/m
u0
Permeability of free space
12.5664e-07 H/m
i, j
sqrt(-1)
1i
Operator Precedence
Measurement expressions are evaluated from left to right, unless there are parentheses.
Operators are listed from higher to lower precedence. Operators on the same line have
the same precedence. For example, a+b*c means a+(b*c), because * has a higher
precedence than +. Similarly, a+b-c means (a+b)-c, because + and - have the same
precedence (and because + is left-associative).
The operators !, &&, and || work with the logical values. The operands are tested for the
values TRUE and FALSE, and the result of the operation is either TRUE or FALSE. In AEL a
logical test of a value is TRUE for non-zero numbers or strings with non-zero length, and
FALSE for 0.0 (real), 0 (integer), NULL or empty strings. Note that the right hand operand
of && is only evaluated if the left hand operand tests TRUE, and the right hand operand of
|| is only evaluated if the left hand operand tests FALSE.
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Measurement Expressions
Operator Precedence
Operator
Name
Example
()
function call, matrix indexer
foo(expr_list)
[]
sweep indexer, sweep
generator
X[expr_list]
{}
matrix generator
{expr_list}
**
exponentiation
expr**expr
!
not
!expr
*
multiply
expr * expr
+
add
expr + expr
::
sequence operator
exp::expr::expr
<
less than
expr < expr
==,EQUALS equal
expr == expr
&& AND
logical and
expr && expr
|| OR
logical or
expr || expr
Conditional Expressions
The if-then-else construct provides an easy way to apply a condition on a per-element
basis over a complete multidimensional variable. It has the following syntax:
A = if ( condition ) then true_expression else false_expression
Condition, true_expression, and false_expression are any valid expressions. The
dimensionality and number of points in these expressions follow the same matching
conditions required for the basic operators.
Multiple nested if-then-else constructs can also be used:
A = if ( condition ) then true_expression elseif ( condition2) then true_expression else
false_expression
The type of the result depends on the type of the true and false expressions. The size of
the result depends on the size of the condition, the true expression, and the false
expression.
Examples
The following information shows several examples of conditional expressions using various
operators.
boolV1=1
boolV2=1
eqOp=if (boolV1 == 1) then 1 else 0 eqOp returns 1
eqOp1=if (boolV1 EQUALS 1) then 1 else 0 eqOp1 returns 1
notEqOp=if (boolV1 != 1) then 1 else 0 notEqOp returns 1
notEqOp1=if (boolV1 NOTEQUALS 1) then 1 else 0 notEqOp1 returns 1
andOp=if (boolV1 == 1 AND boolV2 == 1) then 1 else 0 andOp returns 1
andOp1=if (boolV1 == 1 && boolV2 == 1) then 1 else 0 andOp returns 1
10
Measurement Expressions
orOp=if (boolV1 == 1 OR boolV2 == 1) then 1 else 0 orOp returns 1
orOp1=if (boolV1 == 1 || boolV2 == 1) then 1 else 0 orOp returns 1
Manipulating Simulation Data with Expressions
Expressions defined in this documentation are designed to manipulate data produced by
the simulator. Expressions may reference any simulation output, and may be placed in a
Data Display window. For details on using and applying simulation data with measurement
expressions, refer to Applying Measurements in Preparing a Circuit for Simulation in ADS
(cktsim) of the Using Circuit Simulators (cktsim).
Simulation Data
The expressions package has inherent support for two main simulation data features.
First, simulation data are normally multidimensional. Each sweep introduces a dimension.
All operators and relevant functions are designed to apply themselves automatically over a
multidimensional simulation output. Second, the independent (swept) variable is
associated with the data (for example, S-parameter data). This independent is propagated
through expressions, so that the results of equations are automatically plotted or listed
against the relevant swept variable.
Measurements and Expressions
Measurements are evaluated after a simulation is run and the results are stored in the
dataset. The tag meqn_xxx (where xxx is a number) is placed at the beginning of all
measurement results, to distinguish those results from data produced directly by the
simulator.
Complex measurement equations are available for both circuit and signal processing
simulations. Underlying a measurement is the same generic equations handler that is
available in the Data Display window. Consequently, simulation results can be referenced
directly, and the expression syntax is identical. All operators and almost all functions are
available.
The expression used in an optimization goal or a yield specification is a measurement
expression. It may reference any other measurement on the schematic.
Generating Data
The simulator produces scalars and matrices. When a sweep is being performed, the
sweep can produce scalars and matrices as a function of a set of swept variables. It is also
possible to generate data by using expressions. Two operators can be used to do this. The
first is the sweep generator "[ ]", and the second is the matrix generator "{ }". These
operators can be combined in various ways to produce swept scalars and matrices. The
data can then be used in the normal way in other expressions. The operators can also be
used to concatenate existing data, which can be very useful when combined with the
11
Measurement Expressions
indexing operators.
Sweep Generator Examples
Several sweep generator examples are given below:
arr1=[0,1,2,3,4,5] creates an array of six values
arr2=[0::1::5] generates the above data using the sequence operator
arrCat=[arr1,arr2] concatenates the two arrays
sunArr1=[arr1[3::5],arr1[0::2]] re-arranges the existing data in a different order
z=0*[1::50]
vpadded=[arr1,z] creates a zero-padded array
Matrix Generator Examples
Some examples of the matrix builds operator are given below:
v1={1,2,3,4,5} five-element vector
v2={1::5} five-element vector using the sequence operator
v3=1,0}, {0,1 2X2 identity matrix
Simple Sweeps and Using "[ ]"
Parameter sweeps are commonly used in simulations to generate, for example, a
frequency response or a set of DC IV characteristics. The simulator always attaches the
swept variable to the actual data (the data often being called the attached independent in
equations).
Often after performing a swept analysis we want to look at a single sweep point or a
group of points. The sweep indexer "[ ]" can be used to do this. The sweep indexer is zero
offset, meaning that the first sweep point is accessed as index 0. A sweep of n points can
be accessed by means of an index that runs from 0 to n-1. Also, the what() function can
be useful in indexing sweeps. Use what() to find out how many sweep points there are,
and then use an appropriate index. Indexing out of range yields an invalid result.
The sequence operator can also be used to index into a subsection of a sweep. Given a
parameter X, a subsection of X may be indexed as
a=X[start::increment::stop]
Because increment defaults to one,
a=X[start::stop]
is equivalent to
a=X[start::1::stop]
12
Measurement Expressions
The "::" operator alone is the wildcard operator, so that X and X[::] are equivalent.
Indexing can similarly be applied to multidimensional data. As will be shown later, an
index may be applied in each dimension.
S-Parameters and Matrices
As described above, the sweep indexer "[ ]" is used to index into a sweep. However, the
simulator can produce a swept matrix, as when an S-parameter analysis is performed
over some frequency range. Matrix entries can be referenced as S11 through Snm. While
this is sufficient for most simple applications, it is also possible to index matrices by using
the matrix indexer "()". For example, S(1,1) is equivalent to S11. The matrix indexer is
offset by one meaning the first matrix entry is X(1,1). When it is used with swept data its
operation is transparent with respect to the sweep. Both indexers can be combined. For
example, it is possible to access S(1,1) at the first sweep point as S(1,1)[0]. As with the
sweep indexer "[ ]", the matrix indexer can be used with wild cards and sequences to
extract a submatrix from an original matrix.
Matrices
S-parameters above are an example of a matrix produced by the simulator. Matrices are
more frequently found in signal processing applications. Mathematical operators
implement matrix operations. Element-by-element operations can be performed by using
the dot modified operators (.* and ./).
The matrix indexer conveniently operates over the complete sweep, just as the sweep
indexer operates on all matrices in a sweep. As with scalars, the mathematical operators
allow swept and non-swept quantities to be combined. For example, the first matrix in a
sweep may be subtracted from all matrices in that sweep as
Y = X-X[0]
and Indexing
Multidimensional Sweeps and Indexing
In the previous examples we looked at single-dimensional sweeps. Multidimensional
sweeps can be generated by the simulator by using multiple parameter sweeps.
Expressions are designed to operate on the multidimensional data. Functions and
operators behave in a meaningful way when a parameter sweep is added or taken away. A
common example is DC IV characteristics.
The sweep indexer accepts a list of indices. Up to N indices are used to index Ndimensional data. If fewer than N lookup indices are used with the sweep indexer, then
wild cards are inserted automatically to the left. This is best explained by referring to the
above example files.
User-Defined Functions
13
Measurement Expressions
By writing some Application Extension Language (AEL) code, you can define your own
custom functions. The following file is provided specifically for this purpose:
$HPEESOF_DIR/expressions/ael/user_defined_fun.ael
By reviewing the other _fun.ael files in this directory, you can see how to write your own
code. You can have as many functions as you like in this one file, and they will all be
compiled upon program start-up. If you have a large number of functions to define, you
may want to organize them into more than one file. In this case, include a line such as:
load("more_user_defined_fun.ael");
These load statements are added to the user_defined_fun.ael in the same directory in
order to have your functions all compile. To create your own custom user defined
functions:
1. Copy the $HPEESOF_DIR/expressions/ael/user_defined_fun.ael file to one of the
following directories.
$HOME/hpeesof/expressions/ael (User Config)
$HPEESOF_DIR/custom/expressions/ael (Site Config)
Create the appropriate subdirectories if they do not already exist. The User Config is
setup for a single user. The Site Config can be set up by a CAD Manager or librarian
to control a site configuration for a group of users.
2. Edit the new file and add any custom defined functions. If your custom functions
reside in another file, you can add a load statement to your new user_defined_fun.ael
file to include your functions in another file. For example:
load("my_custom_functions_file.ael");
Save
your changes to the new file and restart so your changes take effect. The
3.
search path looks in the following locations for user defined functions.
$HOME/hpeesof/expressions/ael (User Config)
$HPEESOF_DIR/custom/expressions/ael (Site Config)
$HPEESOF_DIR/expressions/ael (Default Config)
Note
If for some reason your functions are not recognized by the simulator, check to ensure that the
user_defined_fun.atf (compiled version of user_defined_fun.ael file) was generated after restarting
the software.
Functions Reference Format
The information below illustrates how each measurement expression in the functions
reference is described.
<function name>
Presents a brief description of what the function does.
Syntax
Presents the general syntax of the function.
Arguments
Presents a table that includes each argument name, description, range, type, default
value, and whether or not the argument is optional.
Examples
14
Measurement Expressions
Presents one or more simple examples that use the function.
Defined in
Indicates whether the measurement function is defined in a script or is built in. All AEL
functions are built in.
See also
Presents links to related functions, if there are any.
Notes/Equations
Describes any additional notes and/or equations that may help with understanding the
function.
15
Measurement Expressions
Using Measurement Expressions in
Advanced Design System
Measurement Expressions are equations that are used during simulation post processing.
These expressions are entered into the program using the MeasEqn (Measurement
Equation) component, available on the Simulation palettes in an Analog/RF Schematic
window (such as Simulation-AC or Simulation-Envelope), or from the Controllers palette in
a Signal Processing Schematic window.
Many of the more commonly used measurement items are built in, and are found in the
palettes of the appropriate simulator components. Common expressions are included as
measurements, which makes it easy for beginning users to utilize the system. To make
simulation and analyses convenient, all the measurement items, including the built-in
items, can be edited to meet specific requirements. Underlying each measurement is a
function; the functions themselves are available for modification. Moreover, it is also
possible for you to write entirely new measurements and functions.
The measurement items and their underlying expressions are based on Advanced Design
System's Application Extension Language (AEL). Consequently, they can serve a dual
purpose:
They can be used on the schematic page, in conjunction with simulations, to process
the results of a simulation (this is useful, for example, in defining and reaching
optimization goals). Unlike Simulator Expressions, the MeasEqn items are processed
after the simulation engine has finishing its task and just before the dataset is
written.
They can be used in the Data Display window to process the results of a dataset that
can be displayed graphically. Here the MeasEqn items are used to post-process the
data written after simulation is complete.
In either of the above cases, the same syntax is used. However, some measurements
can be used on the schematic page and not the Data Display window, and vice versa.
These distinctions will be noted where they occur.
Note
Not all Measurement Expression Functions have an explicit measurement component. These
functions can be used by means of the MeasEqn component.
MeasEqn(Measurement Equations Component)
For a complete list of Measurement Functions, refer to the Measurement Expressions
(expmeas) in the Advanced Design System.
Symbol
16
Measurement Expressions
Parameters
Instance Name
Displays name of the MeasEqn component in ADS. You can edit the instance name and
place more than one MeasEqn component on the schematic.
Select Parameter
Add
Add an equation to the Select Parameter field.
Cut
Delete an equation from the Select Parameter field.
Paste Copy an equation that has been cut and place it in the Select Parameter field.
Meas
Enter your equation in this field.
Display parameter on schematic
Displays or hides a selected equation on the ADS schematic.
Component Options
For information on this dialog box, refer to " Editing Component Parameters " in the ADS "
Schematic Capture and Layout (usrguide) " documentation.
Notes/Equations
If you are using Advanced Design System, you can place a MeasEqn (Measurement
Equation) component in a schematic window. By placing a MeasEqn component on an ADS
schematic, you can write an equation that can be evaluated, following a simulation, and
displayed in a Data Display window.
17
Measurement Expressions
Note
The if-then-else construct can be used in a MeasEqn component on a schematic. It has the following
syntax: A = if ( condition ) then true_expression else false_expression
18
Measurement Expressions
Circuit Budget Functions
This section describes the circuit budget functions in detail. The functions are listed in
alphabetical order.
bud
bud
bud
bud
bud
bud
bud
bud
bud
bud
bud
bud
bud
bud
freq() (expmeas)
gain() (expmeas)
gain comp() (expmeas)
gamma() (expmeas)
ip3 deg() (expmeas)
nf() (expmeas)
nf deg() (expmeas)
noise pwr() (expmeas)
pwr() (expmeas)
pwr inc() (expmeas)
pwr refl() (expmeas)
snr() (expmeas)
tn() (expmeas)
vswr() (expmeas)
Budget Measurement Analysis
Budget analysis determines the signal and noise performance for elements in the top-level
design. Therefore, it is a key element of system analysis. Budget measurements show
performance at the input and output pins of the top-level system elements. This enables
the designer to adjust, for example, the gains at various components, to reduce nonlinearities. These measurements can also indicate the degree to which a given component
can degrade overall system performance.
Budget measurements are performed upon data generated during a special mode of
circuit simulation. AC and HB simulations are used in budget mode depending upon if
linear or nonlinear analysis is needed for a system design. The controllers for these
simulations have a flag called, OutputBudgetIV which must be set to " yes " for the
generation of budget data. Alternatively, the flag can be set by editing the AC or HB
simulation component and selecting the Perform Budget simulation button on the
Parameters tab.
Budget data contains signal voltages and currents, and noise voltages at every node in the
top level design. Budget measurements are functions that operate upon this data to
characterize system performance parameters including gain, power, and noise figure.
These functions use a constant reference impedance for all nodes for calculations. By
default this impedance is 50 Ohms. The available source power at the input network port
is assumed to equal the incident power at that port.
Budget measurements are available in the schematic and the data display windows. The
budget functions can be evaluated by placing the budget components from Simulation-AC
or Simulation-HB palettes on the schematic. The results of the budget measurements at
the terminal(s) are sorted in ascending order of the component names. The component
names are attached to the budget data as additional dependent variables. To use one of
these measurements in the data display window, first reference the appropriate data in
the default dataset, and then use the equation component to write the budget function.
19
Measurement Expressions
For more detailed information about Budget Measurement Analysis, see Budget Analysis
(cktsim) in Using Circuit Simulators (cktsim).
Note
The budget function can refer only to the default dataset, that is, the dataset selected in the data display
window.
Frequency Plan
A frequency plan of the network is determined for budget mode AC and HB simulations.
This plan tracks the reference carrier frequency at each node in a network. When
performing HB budget, there may be more than one frequency plan in a given network.
This is the case when double side band mixers are used. Using this plan information,
budget measurements are performed upon selected reference frequencies, which can
differ at each node. When mixers are used in an AC simulation, be sure to set the Enable
AC frequency conversion option on the controller, to generate the correct plan.
The budget measurements can be performed on arbitrary networks with multiple signal
paths between the input and output ports. As a result, the measurements can be affected
by reflection and noise generated by components placed between the terminal of interest
and the output port on the same signal path or by components on different signal paths.
Reflection and Backward-Traveling Wave Effects
The effects of reflections and backward-traveling signal and noise waves generated by
components along the signal path can be avoided by inserting a forward-traveling wave
sampler between the components. A forward-traveling wave sampler is an ideal,
frequency-independent directional coupler that allows sampling of forward-traveling
voltage and current waves
This sampler can be constructed using the equation-based linear three-port S-parameter
component. To do this, set the elements of the scattering matrix as follows: S12 = S21 =
S31 = 1 , and all other Sij = 0 . The temperature parameter is set to -273.16 deg C to
make the component noiseless. A noiseless shunt resistor is attached to port 3 to sample
the forward-traveling waves.
bud_freq()
Returns the frequency plan of a network
Syntax
y = bud_freq(freqIn, pinNumber, "simName") for AC analysis or y =
bud_freq(planNumber, pinNumber) for HB analysis
Arguments
20
Measurement Expressions
Name
Description
Default Range Type
Required
freqIn
input source frequency
None
(0:∞)
Real
No
planNumber represents the chosen frequency plan and is required when
using the bud_freq() function with HB data.
None
[1:∞)
Integer Yes
pinNumber
used to choose which pins of each network element are
referenced †
None
[1:∞)
Integer No
simName
simulation instance name, such as "AC1" or "HB1", used to
qualify the data when multiple simulations are performed.
None
None
String
No
† If 1 is passed as the pinNumber, the frequency plan displayed references pin 1 of each
element; otherwise, the frequency plan is displayed for all pins of each element. (Note
that this means it is not possible to select only pin 2 of each element, for example.) By
default, the frequency plan is displayed for pin 1 of each element.
Examples
x = bud_freq()
Returns frequency plan for AC analysis.
x = bud_freq(1MHz)
Returns frequency plan for frequency swept AC analysis. By passing the value of
1MHz the plan is returned for the subset of the sweep, when the source value is
1MHz
x = bud_freq(2)
For HB, returns a selected frequency plan, 2, with respect to pin 1 of every
network element.
Defined in
$HPEESOF_DIR/expressions/ael/budget_fun.ael
Notes/Equations
Used in AC and harmonic balance (HB) simulations.
This function is used in AC and HB simulations with the budget parameter turned on. For
AC, the options are to pass no parameters, or the input source frequency (freqIn), for the
first parameter if a frequency sweep is performed. freqIn can still be passed if no sweep is
performed, table data is just formatted differently. The first argument must be a real
number for AC data and the second argument is an integer, used optionally to choose pin
references.
When a frequency sweep is performed in conjunction with AC, the frequency plan of a
particular sweep point can be chosen.
For HB, this function determines the fundamental frequencies at the terminal(s) of each
component, thereby given the entire frequency plan for a network. Sometimes more than
one frequency plan exists in a network. For example when double sideband mixers are
used. This function gives the user the option of choosing the frequency plan of interest.
Note that a negative frequency at a terminal means that a spectral inversion has occurred
at the terminal. For example, in frequency-converting AC analysis, where vIn and vOut
are the voltages at the input and output ports, respectively, the relation may be either
vOut=alpha*vIn if no spectral inversion has occurred, or vOut=alpha*conj(vIn) if there
was an inversion. Inversions may or may not occur depending on which mixer sidebands
21
Measurement Expressions
one is looking at.
Note
Remember that the budget function can refer only to the default dataset, that is, the dataset selected in
the data display window.
Budget Path Measurements
Instead of all components in alphabetical order, this function can report its values just for
the components selected in a budget path, and following the sequence in that path. To
facilitate the budget path measurements the name of the budget path variable, as defined
in the Schematic window, needs to be entered as the pinNumber argument.
bud_gain()
Returns budget transducer-power gain
Syntax
y = bud_gain(vIn, iIn, Zs, Plan, pinNumber, "simName") or y = bud_gain("SourceName",
SrcIndx, Zs, Plan, budgetPath)
Arguments
Name
Description
Default Range Type
vIn
voltage flowing into the input port
None
(∞:∞)
Complex Yes
Required
iIn
current flowing into the input port
None
(∞:∞)
Complex Yes
SourceName component name at the input port
None
None
String
Yes
SrcIndx †
frequency index that corresponds to the source frequency 1
to determine which frequency to use from a multitone
source as the reference signal
[1:∞)
Integer
No
Zs
input source port impedance
50.0
[0:∞)
Real
No
Plan †
number of the selected frequency plan(needed only for
HB)
None
None
String
No
pinNumber
Used to choose which pins of each network element are
referenced ††
1
[1:∞)
Integer
No
budgetPath
Selects the budget path, specified as an array eg.
["PORT1.t1","Tee1.t3","Term3.t1"]
None
None
String
Array
No
simName
simulation instance name, such as "AC1" or "HB1", used
to qualify the data when multiple simulations are
performed.
None
None
String
No
† Note that for AC simulation, both the SrcIndx and Plan arguments must not be
specified; these are for HB only.
†† If 1 is passed as the pinNumber, the results at pin 1 of each element are returned;
otherwise, the results for all pins of each element are returned. By default, the pinNumber
is set to 1.
Examples
x = bud_gain(PORT1.t1.v, PORT1.t1.i)
or
22
Measurement Expressions
x = bud_gain("PORT1")
y= bud_gain(PORT1.t1.v, PORT1.t1.i, 75)
or
y= bud_gain("PORT1", , 75., 1)
z = bud_gain(PORT1.t1.v[3], PORT1.t1.i[3], , 1)
or
z= bud_gain("PORT1", 3, , 1)
Defined in
$HPEESOF_DIR/expressions/ael/budget_fun.ael
See Also
bud_gain_comp() (expmeas)
Notes/Equations
Used in AC and harmonic balance simulations
This is the power gain (in dB) from the input port to the terminal(s) of each component,
looking into that component. Power gain is defined as power delivered to the resistive load
minus the power available from the source. Note that the fundamental frequency at
different pins can be different. If vIn and iIn are passed directly, one may want to use the
index of the frequency sweep explicitly to reference the input source frequency.
Note
Remember that the budget function can refer only to the default dataset, that is, the dataset selected in
the data display window.
Budget Path Measurements
Instead of all components in alphabetical order, this function can report its values just for
the components selected in a budget path, and following the sequence in that path. To
facilitate the budget path measurements, the name of the budget path variable (as
defined in the Schematic window), must be entered as the budgetPath argument. Use the
alternate syntax for budget path measurements as shown below.
bud_gain("SourceName", SrcIndx, Zs, Plan, budgetPath)
bud_gain_comp()
Returns budget gain compression at fundamental frequencies as a function of power.
Syntax
y = bud_gain_comp(vIn, iIn, Zs, Plan, freqIndex, pinNumber, "simName") or y =
bud_gain_comp("SourceName", SrcIndx, Zs, Plan, freqIndex, pinNumber, "simName")
Arguments
23
Measurement Expressions
Name
Description
Default Range Type
Required
vIn
voltage flowing into the input port
None
(∞:∞)
Complex Yes
iIn
current flowing into the input port
None
(∞:∞)
Complex Yes
SourceName component name at the input port
None
None
String
Yes
SrcIndx †
frequency index that corresponds to the source frequency
to determine which frequency to use from a multitone
source as the reference signal
1
[1:∞)
Integer
No
Zs
input source port impedance
50.0
[0:∞)
Real
No
freqIndex † index of harmonic frequency
None
(∞:∞)
Integer
No
Plan ††
number of the selected frequency plan(needed only for
HB)
None
None
String
No
pinNumber
Used to choose which pins of each network element are
referenced † ††
1
[1:∞)
Integer
No
simName
simulation instance name, such as "AC1" or "HB1", used to None
qualify the data when multiple simulations are performed.
None
String
No
† Used if Plan is not selected.
†† Note that for AC simulation, both the SrcIndx and Plan arguments must not be
specified; these are for HB only.
† †† If 1 is passed as the pinNumber, the results at pin 1 of each element are returned;
otherwise, the results for all pins of each element are returned. By default, the pinNumber
is set to 1.
Examples
x = bud_gain_comp(PORT1.t1.v[3], PORT1.t1.i[3], , 1)
x = bud_gain_comp("PORT1", 3, , 1)
returns the gain compression at the fundamental frequencies as a function of
power.
y= bud_gain_comp(PORT1.t1.v[3], PORT1.t1.i[3], , , 1)
y= bud_gain_comp("PORT1", 3, , , 1)
returns the gain compression at the second harmonic frequency as a function of
power.
Defined in
$HPEESOF_DIR/expressions/ael/budget_fun.ael
See Also
bud_gain() (expmeas)
Notes/Equations
Used in Harmonic balance simulation with sweep
This is the gain compression (in dB) at the given input frequency from the input port to
24
Measurement Expressions
the terminal(s) of each component, looking into that component. Gain compression is
defined as the small signal linear gain minus the large signal gain. Note that the
fundamental frequency at each element pin can be different by referencing the frequency
plan. A power sweep of the input source must be used in conjunction with HB. The first
power sweep point is assumed to be in the linear region of operation.
Note
Remember that the budget function can refer only to the default dataset, that is, the dataset selected in
the data display window.
Budget Path Measurements
This function does not support the budget path feature.
bud_gamma()
Returns the budget reflection coefficient.
Syntax
y = bud_gamma(Zref, Plan, pinNumber, "simName")
Arguments
Name
Description
Default Range Type
Required
Zref
input source port impedance
50.0
[0:∞)
Real
No
Plan †
number of the selected frequency plan(needed only for HB)
None
None
String
No
pinNumber Used to choose which pins of each network element are
referenced ††
1
[1:∞)
Integer No
simName
None
None
String
simulation instance name, such as "AC1" or "HB1", used to
qualify the data when multiple simulations are performed.
No
† Note that for AC simulation, both the SrcIndx and Plan arguments must not be
specified; these are for HB only.
†† If 1 is passed as the pinNumber, the results at pin 1 of each element are returned;
otherwise, the results for all pins of each element are returned. By default, the pinNumber
is set to 1.
Examples
x = bud_gamma()
returns reflection coefficient at all frequencies.
y = bud_gamma(75, 1)
returns reflection coefficient at reference frequencies in plan 1
Defined in
$HPEESOF_DIR/expressions/ael/budget_fun.ael
See Also
25
bud_vswr() (expmeas)
Measurement Expressions
Notes/Equations
Used in AC and harmonic balance simulations
This is the complex reflection coefficient looking into the terminal(s) of each component.
Note that the fundamental frequency at different pins can in general be different, and
therefore values are given for all frequencies unless a Plan is referenced.
Note
Remember that the budget function can refer only to the default dataset, that is, the dataset selected in
the data display window.
Budget Path Measurements
Instead of all components in alphabetical order, this function can report its values just for
the components selected in a budget path, and following the sequence in that path. To
facilitate the budget path measurements the name of the budget path variable, as defined
in the Schematic window, needs to be entered as the pinNumber argument.
bud_ip3_deg()
Returns the budget third-order intercept point degradation
Syntax
y = bud_ip3_deg(vOut, LinearizedElement, fundFreq, imFreq, zRef)
Arguments
Name
Description
Default Range Type
Required
vOut
signal voltage at the output
None
(∞:∞)
Real,
Complex
Yes
LinearizedElement variable containing the names of the linearized
components
None
None
String
Yes
fundFreq
harmonic frequency indices for the fundamental
frequency
None
(∞:∞)
Integer
Yes
imFreq
harmonic frequency indices for the
intermodulation frequency
None
(∞:∞)
Integer
Yes
Zref
input source port impedance
50.0
[0:∞)
Real
No
Examples
y = bud_ip3_deg(vOut, LinearizedElement, {1, 0}, {2, -1})
returns the budget third-order intercept point degradation
Defined in
$HPEESOF_DIR/expressions/ael/budget_fun.ael
26
Measurement Expressions
See Also
ip3_out() (expmeas), ipn() (expmeas)
Notes/Equations
Used in Harmonic balance simulation with the BudLinearization Controller.
This measurement returns the budget third-order intercept point degradation from the
input port to any given output port. It does this by setting to linear each component in the
top-level design, one at a time.
For the components that are linear to begin with, this measurement will not yield any
useful information. For the nonlinear components, however, this measurement will
indicate how the nonlinearity of a certain component degrades the overall system IP3. To
perform this measurement, the BudLinearization Controller needs to be placed in the
schematic window. If no component is specified in this controller, all components on the
top level of the design are linearized one at a time, and the budget IP3 degradation is
computed.
Budget Path Measurements
This function does not support the budget path feature.
bud_nf()
Returns the budget noise figure
Syntax
y = bud_nf(vIn, iIn, noisevIn) or y=bud_nf("SourceName",Zs,BW,pinNumber,"simName")
Arguments
Name
Description
Default Range Type
Required
vIn
voltage flowing into the input port
None
(∞:∞)
Complex Yes
iIn
current flowing into the input port
None
(∞:∞)
Complex Yes
noisevIn
noise input at the input port
None
(∞:∞)
Complex Yes
SourceName component name at the input port
None
None
String
Yes
Zs
input source port impedance
50.0
[0:∞)
Real
No
BW †
bandwidth
1
[1:∞)
Real
No
pinNumber
Used to choose which pins of each network element are
referenced ††
1
[1:∞)
Integer
No
simName
simulation instance name, such as "AC1" or "HB1", used to None
qualify the data when multiple simulations are performed.
None
String
No
† BW must be set as the value of Bandwidth used on the noise page of the AC controller
†† If 1 is passed as the pinNumber, the results at pin 1 of each element are returned;
otherwise, the results for all pins of each element are returned. By default, the pinNumber
27
is set to 1.
Measurement Expressions
Examples
x = bud_nf(PORT1.t1.v, PORT1.t1.i, PORT1.t1.v.noise)
x = bud_nf("PORT1")
In an AC analysis, bud_nf() can be used as below:
BudNF1=bud_nf("PORT1")
BudNF2=bud_nf("PORT1",50.0,1 Hz,2,"AC1")
BudNF3=bud_nf("PORT1",,,,,budget_path)
BudNF4=bud_nf(,,,,,budget_path)
where budget_path could be defined as:
budget_path =
["PORT1.t1","b2_AMP1.t2","b3_MIX1.t2","b4_AMP2.t2","b5_BPF2.t2","b6.t1"]
Defined in
$HPEESOF_DIR/expressions/ael/budget_fun.ael
See Also
bud_nf_deg() (expmeas), bud_tn() (expmeas)
Notes/Equations
Used in AC simulation
This is the noise figure (in dB) from the input port to the terminal(s) of each component,
looking into that component. The noise analysis control parameters in the AC Simulation
component must be selected: "Calculate Noise" and "Include port noise". For the source,
the parameter "Noise" should be set to yes. The noise figure is always calculated per IEEE
standard definition with the input termination at 290 K.
Note
Remember that the budget function can refer only to the default dataset, that is, the dataset selected in
the data display window.
Budget Path Measurements
Instead of all components in alphabetical order, this function can report its values just for
the components selected in a budget path, and following the sequence in that path. To
facilitate the budget path measurements the name of the budget path variable, as defined
in the Schematic window, needs to be entered as the pinNumber argument.
bud_nf_deg()
Returns budget noise figure degradation
Syntax
28
Measurement Expressions
y = bud_nf_deg(vIn, iIn, vOut, iOut, vOut.NC.vnc, vOut.NC.name, Zs, BW)
y = bud_nf_deg("PORT1", "Term1", "vOut")
Arguments
Name
Description
Default Range Type
Required
vIn
voltage flowing into the input port
None
(∞:∞)
Complex Yes
iIn
current flowing into the input port
None
(∞:∞)
Complex Yes
vOut
voltage flowing into the output port
None
(∞:∞)
Complex Yes
iOut
current flowing into the output port
None
(∞:∞)
Complex Yes
vOut.NC.vnc
noise contributions at the output port
None
None
String
Yes
vOut.NC.name noise contributions component names at the output port None
None
String
Yes
Zs
input source port impedance
50.0
[0:∞)
Real
No
BW †
bandwidth
1
[1:∞)
Real
No
† BW must be set as the value of Bandwidth used on the noise page of the AC controller
Examples
x = bud_nf_deg(PORT1.t1.v, PORT1.t1.i, Term1.t1.v, Term1.t1.i, vOut.NC.vnc,
vOut.NC.name)
x = bud_nf_deg("PORT1", "Term1", "vOut")
Defined in
$HPEESOF_DIR/expressions/ael/budget_fun.ael
See Also
bud_nf() (expmeas), bud_tn() (expmeas)
Notes/Equations
Used in AC simulation
The improvement of system noise figure is given when each element is made noiseless.
This is the noise figure (in dB) from the source port to a specified output port, obtained
while setting each component noiseless, one at a time. The noise analysis and noise
contribution control parameters in the AC Simulation component must be selected. For
noise contribution, the output network node must be labeled and referenced on the noise
page in the AC Controller. Noise contributors mode should be set to "Sort by Name." The
option "Include port noise "on the AC Controller should be selected. For the source, the
parameter "Noise" should be set to yes. For this particular budget measurement the AC
controller parameter "OutputBudgetIV" can be set to no. The noise figure is always
calculated per IEEE standard definition with the input termination at 290 K.
29
Measurement Expressions
Note
Remember that the budget function can refer only to the default dataset, that is, the dataset selected in
the data display window.
Budget Path Measurements
This function does not support the budget path feature.
bud_noise_pwr()
Returns the budget noise power
Syntax
y = bud_noise_pwr(Zref, Plan, pinNumber, "simName")
Arguments
Name
Description
Default Range Type
Required
Zref
input source port impedance
50.0
[0:∞)
Real
No
Plan
number of the selected frequency plan(needed only for HB)
None
None
String
No
pinNumber Used to choose which pins of each network element are
referenced †
1
[1:∞)
Integer No
simName
None
None
String
simulation instance name, such as "AC1" or "HB1", used to
qualify the data when multiple simulations are performed.
No
† If 1 is passed as the pinNumber, the results at pin 1 of each element are returned;
otherwise, the results for all pins of each element are returned. By default, the pinNumber
is set to 1.
Examples
x = bud_noise_pwr() returns the noise power at all frequencies
y = bud_noise_pwr(75, 1) returns the noise power at reference frequencies in
plan 1
Defined in
$HPEESOF_DIR/expressions/ael/budget_fun.ael
See Also
bud_pwr() (expmeas)
Notes/Equations
Used in AC and harmonic balance simulations
This is the noise power (in dBm) at the terminal(s) of each component, looking into the
component. If Zref is not specified, the impedance that relates the signal voltage and
30
Measurement Expressions
current is used to calculate the noise power. Note that the fundamental frequency at
different pins can be different, and therefore values are given for all frequencies unless a
Plan is referenced.
Note
Remember that the budget function can refer only to the default dataset, that is, the dataset selected in
the data display window.
This function does not have the bandwidth parameter, so the results rely entirely on the
setting of the bandwidth in the Noise tab of the simulation controller.
For AC noise and budget calculations, the bandwidth parameter flatly scales the noise
voltages, and consequently noise powers, SNR, etc., regardless of the frequency response.
If you make a frequency sweep then the narrow band noise voltages properly follow the
frequency characteristic of the circuit and are presented as a function of the swept
frequency values. However, changing the bandwidth in the simulator controller would
again just flatly rescale all the values, regardless of whether the frequency response
remains flat or changes drastically over the (local) bandwidth, or whether the adjacent
bands overlap or not.
The only true integration over a bandwidth is done for the phase noise (as one of the
options in the NoiseCon controller).
A work-around solution is to do an appropriately wide frequency sweep setting the
bandwidth value in the AC controller to that of the frequency step. Then adding all the
powers (need to be first converted from dBm to watts) would do the integration.
Budget Path Measurements
Instead of all components in alphabetical order, this function can report its values just for
the components selected in a budget path, and following the sequence in that path. To
facilitate the budget path measurements the name of the budget path variable, as defined
in the Schematic window, needs to be entered as the pinNumber argument.
bud_pwr()
Returns the budget signal power in dBm
Syntax
y = bud_pwr(Plan, pinNumber, "simName")
Arguments
Name
Description
Default Range Type
Required
Plan
number of the selected frequency plan(needed only for HB)
None
None
String
No
pinNumber Used to choose which pins of each network element are
referenced †
1
[1:∞)
Integer No
simName
None
None
String
simulation instance name, such as "AC1" or "HB1", used to
qualify the data when multiple simulations are performed.
No
† If 1 is passed as the pinNumber, the results at pin 1 of each element are returned;
otherwise, the results for all pins of each element are returned. By default, the pinNumber
is set to 1.
Examples
31
Measurement Expressions
x = bud_pwr() returns the signal power at all frequencies when used in AC or HB
simulations
y = bud_pwr(50, 1) returns the signal power at reference frequencies in plan 1
when used for HB simulations
Defined in
$HPEESOF_DIR/expressions/ael/budget_fun.ael
See Also
bud_noise_pwr() (expmeas)
Notes/Equations
Used in AC and harmonic balance simulations.
This is the signal power (in dBm) at the terminal(s) of each component, looking into the
component. Note that the fundamental frequency at different pins can be different, and
therefore values are given for all frequencies unless a Plan is referenced.
Note
Remember that the budget function can refer only to the default dataset, that is, the dataset selected in
the data display window.
Budget Path Measurements
Instead of all components in alphabetical order, this function can report its values just for
the components selected in a budget path, and following the sequence in that path. To
facilitate the budget path measurements the name of the budget path variable, as defined
in the Schematic window, needs to be entered as the pinNumber argument.
bud_pwr_inc()
Returns the budget incident power.
Syntax
y = bud_pwr_inc(Zref, Plan, pinNumber, "simName")
Arguments
32
Measurement Expressions
Name
Description
Default Range Type
Required
Zref
input source port impedance
50.0
[0:∞)
Real
No
Plan
number of the selected frequency plan(needed only for HB)
None
None
String
No
pinNumber Used to choose which pins of each network element are
referenced †
1
[1:∞)
Integer No
simName
None
None
String
simulation instance name, such as "AC1" or "HB1", used to
qualify the data when multiple simulations are performed.
No
† If 1 is passed as the pinNumber, the results at pin 1 of each element are returned;
otherwise, the results for all pins of each element are returned. By default, the pinNumber
is set to 1.
Examples
x = bud_pwr_inc() returns incident power at all frequencies
y = bud_pwr_inc(75, 1) returns incident power at reference frequencies in plan
1
Defined in
$HPEESOF_DIR/expressions/ael/budget_fun.ael
See Also
bud_pwr_refl() (expmeas)
Notes/Equations
Used in AC and harmonic balance simulations
This is the incident power (in dBm) at the terminal(s) of each component, looking into the
component. Note that the fundamental frequency at different pins can be different, and
therefore values are given for all frequencies unless a Plan is referenced.
Note
Remember that the budget function can refer only to the default dataset, that is, the dataset selected in
the data display window.
Budget Path Measurements
Instead of all components in alphabetical order, this function can report its values just for
the components selected in a budget path, and following the sequence in that path. To
facilitate the budget path measurements the name of the budget path variable, as defined
in the Schematic window, needs to be entered as the pinNumber argument.
bud_pwr_refl()
Returns the budget reflected power
Syntax
33
Measurement Expressions
Syntax
y = bud_pwr_refl(Zref, Plan, pinNumber, "simName")
Arguments
Name
Description
Default Range Type
Required
Zref
input source port impedance
50.0
[0:∞)
Real
No
Plan
number of the selected frequency plan(needed only for HB)
None
None
String
No
pinNumber Used to choose which pins of each network element are
referenced †
1
[1:∞)
Integer No
simName
None
None
String
simulation instance name, such as "AC1" or "HB1", used to
qualify the data when multiple simulations are performed.
No
† If 1 is passed as the pinNumber, the results at pin 1 of each element are returned;
otherwise, the results for all pins of each element are returned. By default, the pinNumber
is set to 1.
Examples
x = bud_pwr_refl() returns reflected power at all frequencies
y = bud_pwr_refl(75, 1) returns reflected power at reference frequencies in
plan 1
Defined in
$HPEESOF_DIR/expressions/ael/budget_fun.ael
See Also
bud_pwr_inc() (expmeas)
Notes/Equations
Used in AC and harmonic balance simulations
This is the reflected power (in dBm) at the terminal(s) of each component, looking into
the component. Note that the fundamental frequency at different pins can be different,
and therefore values are given for all frequencies unless a Plan is referenced.
Note
Remember that the budget function can refer only to the default dataset, that is, the dataset selected in
the data display window.
Budget Path Measurements
Instead of all components in alphabetical order, this function can report its values just for
the components selected in a budget path, and following the sequence in that path. To
facilitate the budget path measurements the name of the budget path variable, as defined
34
Measurement Expressions
in the Schematic window, needs to be entered as the pinNumber argument.
bud_snr()
Returns the budget signal-to-noise-power ratio
Syntax
y = bud_snr(Plan, pinNumber, "simName")
Arguments
Name
Description
Default Range Type
Required
Plan
number of the selected frequency plan(needed only for HB)
None
None
String
No
pinNumber Used to choose which pins of each network element are
referenced †
1
[1:∞)
Integer No
simName
None
None
String
simulation instance name, such as "AC1" or "HB1", used to
qualify the data when multiple simulations are performed.
No
† If 1 is passed as the pinNumber, the results at pin 1 of each element are returned;
otherwise, the results for all pins of each element are returned. By default, the pinNumber
is set to 1.
Examples
x = bud_snr() returns the SNR at all frequencies
y = bud_snr(1) returns the SNR at reference frequencies in plan 1
Defined in
$HPEESOF_DIR/expressions/ael/budget_fun.ael
Notes/Equations
Used in AC and harmonic balance simulations
This is the SNR (in dB) at the terminal(s) of each component, looking into that
component. Note that the fundamental frequency at different pins can in general be
different, and therefore values are given for all frequencies unless a Plan is referenced.
The noise analysis control parameter in the AC and Harmonic Balance Simulation
components must be selected. For the AC Simulation component select: "Calculate Noise"
and "Include port noise." For the source, the parameter "Noise" should be set to yes. In
Harmonic Balance select the "Nonlinear noise" option.
Note
Remember that the budget function can refer only to the default dataset, that is, the dataset selected in
the data display window.
Budget Path Measurements
Instead of all components in alphabetical order, this function can report its values just for
the components selected in a budget path, and following the sequence in that path. To
35
Measurement Expressions
facilitate the budget path measurements the name of the budget path variable, as defined
in the Schematic window, needs to be entered as the pinNumber argument.
bud_tn()
Returns the budget equivalent output-noise temperature
Syntax
y = bud_tn(vIn, iIn, noisevIn, Zs, BW, pinNumber, "simName") or y =
bud_tn("SourceName")
Arguments
Name
Description
Default Range Type
vIn
voltage flowing into the input port
None
(∞:∞)
Complex Yes
iIn
current flowing into the input port
None
(∞:∞)
Complex Yes
noisevIn
noise input at the input port
None
(∞:∞)
Complex Yes
Zs
input source port impedance
50.0
[0:∞)
Real
No
BW †
bandwidth
1
[1:∞)
Real
No
pinNumber
Used to choose which pins of each network element are
referenced ††
1
[1:∞)
Integer
No
simName
simulation instance name, such as "AC1" or "HB1", used to None
qualify the data when multiple simulations are performed.
None
String
No
None
String
Yes
SourceName component name at the input port
None
Required
† BW must be set as the value of Bandwidth used on the noise page of the AC controller
†† If 1 is passed as the pinNumber, the results at pin 1 of each element are returned;
otherwise, the results for all pins of each element are returned. By default, the pinNumber
is set to 1.
Examples
x = bud_tn(PORT1.t1.v, PORT1.t1.i, PORT1.t1.v.noise)
x = bud_tn("PORT1")
Defined in
$HPEESOF_DIR/expressions/ael/budget_fun.ael
See Also
bud_nf() (expmeas), bud_nf_deg() (expmeas)
Notes/Equations
Used in AC simulation
36
Measurement Expressions
This is an equivalent output-noise temperature (in Kelvin) from the input port to the
terminal(s) of each component, looking into that component. The noise analysis and noise
contribution control parameters in the AC Simulation component must be selected:
"Calculate Noise" and "Include port noise." For the source, the parameter "Noise" should
be set to yes. The output-noise temperature is always calculated per IEEE standard
definition with the input termination at 290 K.
Note
Remember that the budget function can refer only to the default dataset, that is, the dataset selected in
the data display window.
Budget Path Measurements
Instead of all components in alphabetical order, this function can report its values just for
the components selected in a budget path, and following the sequence in that path. To
facilitate the budget path measurements the name of the budget path variable, as defined
in the Schematic window, needs to be entered as the pinNumber argument.
bud_vswr()
Returns the budget voltage-standing-wave ratio
Syntax
y = bud_vswr(Zref, Plan, pinNumber, "simName")
Arguments
Name
Description
Default Range Type
Required
Zref
input source port impedance
50.0
[0:∞)
Real
No
Plan
number of the selected frequency plan(needed only for HB)
None
None
String
No
pinNumber Used to choose which pins of each network element are
referenced †
1
[1:∞)
Integer No
simName
None
None
String
simulation instance name, such as "AC1" or "HB1", used to
qualify the data when multiple simulations are performed.
No
† If 1 is passed as the pinNumber, the results at pin 1 of each element are returned;
otherwise, the results for all pins of each element are returned. By default, the pinNumber
is set to 1.
Examples
x = bud_vswr() returns the vswr at all frequencies
y = bud_vswr(75, 1) returns the vswr at reference frequencies in plan 1
Defined in
$HPEESOF_DIR/expressions/ael/budget_fun.ael
See Also
37
bud_gamma() (expmeas)
Measurement Expressions
Notes/Equations
Used in AC and harmonic balance simulations
This is the VSWR looking into the terminal(s) of each component. Note that the
fundamental frequency at different pins can be different, and therefore values are given
for all frequencies unless a Plan is referenced.
Note
Remember that the budget function can refer only to the default dataset, that is, the dataset selected in
the data display window.
Budget Path Measurements
Instead of all components in alphabetical order, this function can report its values just for
the components selected in a budget path, and following the sequence in that path. To
facilitate the budget path measurements the name of the budget path variable, as defined
in the Schematic window, needs to be entered as the pinNumber argument.
38
Measurement Expressions
Circuit Envelope Functions
This section describes the circuit envelope functions in detail. The functions are listed in
alphabetical order.
ACPR ChPwr or EVM from 1tone swp() (expmeas)
acpr vi() (expmeas)
acpr vr() (expmeas)
channel power vi() (expmeas)
channel power vr() (expmeas)
const evm() (expmeas)
cross hist() (expmeas)
delay path() (expmeas)
evm wlan dsss cck pbcc() (expmeas)
evm wlan ofdm() (expmeas)
fs() (expmeas)
Mod Data from 1tone swpUNI() (expmeas)
peak pwr() (expmeas)
peak to avg pwr() (expmeas)
power ccdf() (expmeas)
power ccdf ref() (expmeas)
pwr vs t() (expmeas)
relative noise bw() (expmeas)
sample delay pi4dqpsk() (expmeas)
sample delay qpsk() (expmeas)
spectrum analyzer() (expmeas)
total pwr() (expmeas)
trajectory() (expmeas)
Working with Envelope Data
Circuit Envelope Analysis produces complex frequency spectra as a function of time. A
single envelope analysis can produce 2-dimensional data where the outermost
independent variable is time and the innermost is frequency or harmonic number.
Indexing can be used to look at a harmonic against time, or a spectrum at a particular
time index.
ACPR_ChPwr_or_EVM_from_1tone_swp()
Returns an amplifier's adjacent or alternate channel power ratios, or main channel power,
or error vector magnitude
Syntax
ACPR_ChPwr_or_EVM_from_1tone_swp(returnVal, algorithm, allowextrap, charVoltage,
inputSig, sourceZ, loadZ, mainCh, lowerAdjCh, upperAdjCh, winType, winConst)
Arguments
39
Measurement Expressions
Name
Description
Default
Range
Type
Required
returnVal
Specifies what the function is to return. Use
"ACPR" for Adjacent (or Alternate) Channel
Power Ratio (dBc), "MAINCHP" for Main
Channel Power (dBm), or "EVM" for Error
Vector Magnitude (%).
None
"ACPR",
"MAINCHP", or
"EVM"
String
Yes
algorithm
Specifies the algorithm to be used to model
None
the vout-versus-vin data from the HB sweep.
Use "CF" for Curve Fit or "LI" for Linear
Interpolation.
"LI" or "CF"
String
Yes
allowextrap Allow or disallow extrapolation when applying 1
the scaled, modulated input signal to the
vout-versus-vin model.
0, "No", "NO",
"no", 1, "Yes",
"YES", "yes"
String or
Integer
No
charVoltage This is the characterization voltage (the
fundamental output voltage from the
harmonic balance sweep.) Example:
Vload_fund, where Vload_fund=Vload[1].
None
(-∞:∞)
Complex
Yes
inputSig
This is the input modulated signal (the
None
envelope.) This signal should be a function of
time, only.
(-∞:∞)
Complex
Yes
sourceZ
This is the source impedance. This can be a
swept parameter.
None
(0:∞)
Complex
Yes
loadZ
This is the load impedance. This can be a
swept parameter.
None
(0:∞)
Complex
Yes
mainCh
These are the main channel frequency limits, None
as an offset from the carrier frequency.
Example: {(-3.84 MHz/2),(3.84 MHz/2)}
(-∞:∞)
1X2
matrix,
Real or
Integer
Yes
lowerAdjCh These are the lower adjacent (or alternate)
None
channel frequency limits as an offset from the
carrier frequency. Example: MainLimits - (5
MHz)
(-∞:∞)
1X2
matrix,
Real or
Integer
Yes
upperAdjCh These are the upper adjacent (or alternate)
None
channel frequency limits as an offset from the
carrier frequency. Example: MainLimits + (5
MHz)
(-∞:∞)
1X2
matrix,
Real or
Integer
Yes
winType
window type
†
string
No
winConst
window constant that affects the shape of the depends
applied window.
on
winType
used
[0:∞)
Real
No
"Kaiser"
† winType can be: "none", "hamming", "hanning", "gaussian", "kaiser", "8510",
"blackman","blackman-harris"
Examples
Vload_fundHB=Vload[1]
Vin_fund=_3GPPFDD_UE_Tx_12_2_SigGen..Vsource
Zsource=50
Zload=50
MainLimits={-3.84 MHz/2,3.84 MHz/2}
LoChLimits=MainLimits-(5 MHz)
UpChLimits=MainLimits+(5 MHz)
LoChLimitsAlt=MainLimits-(10 MHz)
UpChLimitsAlt=MainLimits+(10 MHz)
ACPR_dBc=ACPR_ChPwr_or_EVM_from_1tone_swp("ACPR", "LI", "Yes", Vload_fundHB,
40
Measurement Expressions
Vin_fund, Zsource, Zload, MainLimits, LoChLimits, UpChLimits, "Kaiser",)
AltCPR_dBc=ACPR_ChPwr_or_EVM_from_1tone_swp("ACPR", "LI", "Yes", Vload_fundHB,
Vin_fund, Zsource, Zload, MainLimits, LoChLimitsAlt, UpChLimitsAlt, "Kaiser",)
Pout_dBm=ACPR_ChPwr_or_EVM_from_1tone_swp("MAINCHP", "LI", "Yes", Vload_fundHB,
Vin_fund, Zsource, Zload, MainLimits, LoChLimits, UpChLimits, "Kaiser",)
ACPR_vs_Pout=vs(ACPR_dBc,Pout_dBm)
AltCPR_vs_Pout=vs(AltCPR_dBc,Pout_dBm)
EVM_percent=ACPR_ChPwr_or_EVM_from_1tone_swp("EVM", "LI", "Yes", Vload_fundHB,
Vin_fund, Zsource, Zload, MainLimits, LoChLimits, UpChLimits, "Kaiser",)
EVM_vs_Pout=vs(EVM_percent,Pout_dBm)
See Also
Mod_Data_from_1toneSwpUNI() (expmeas)
Notes/Equations
This function returns the adjacent or alternate channel power ratio (in dBc), main channel
power (in dBm), or EVM in percent.
It can be used in a measurement expression in a schematic or in the data display. While it
is slower to use the ACPR_ChPwr_or_EVM_from_1tone_swp() function on the schematic
than the Mod_Data_from_1tone_swpUNI() in the data display, the advantage is that the
results are written into the dataset, and data displays that show these results open
instantly.
However, when using ACPR_ChPwr_or_EVM_from_1tone_swp(), you have to call it once
to get the adjacent channel power ratios, once again to get the alternate channel power
ratios, once again to get the main channel power, and once again to get the EVM. The big
disadvantage of using the Mod_Data_from_1tone_swpUNI() is that this function will get
executed each time you open a data display that contains it.
For EVM, this single-tone method is not specification-compliant. It just measures the
“raw” EVM, computed at each time point. The EVM is computed after correcting for the
average phase difference and RMS amplitude difference between the output and input
modulated signals. If the modulated signal at the output of the amplifier has only a
constant phase shift and a constant gain (meaning that neither vary with the amplitude of
the input modulated signal), then the EVM will be zero. With this method, the EVM is
computed at each time point, not at just the symbol times. There is no demodulation or
decoding of the signal, so you can’t calculate the EVM of each sub-carrier, say for an LTE
signal.
For ACPR, this single-tone method does not include any receive-side filtering. It just
generates the spectrum at the output of the amplifier, integrates the power in the main,
adjacent, and alternate channels, then computes the ratios. The single-tone method of
computing EVM (and ACPR) will tend to become less accurate as the bandwidth of the
41
Measurement Expressions
signal gets larger. This is because this method assumes the response of the amplifier is
constant across the modulation bandwidth (we’re modeling the nonlinearity by injecting a
single tone at the carrier frequency, after all.)
acpr_vi()
Computes the adjacent-channel power ratio following a Circuit Envelope simulation
Syntax
ACPRvals = acpr_vi(voltage, current, mainCh, lowerAdjCh, upperAdjCh, winType,
winConst)
Arguments
Name
Description
Default Range Type
voltage
single complex voltage spectral component (for example,
the fundamental) across a load versus time
None
(∞:∞)
Complex Yes
current
single complex current spectral component into the same
load versus time
None
(∞:∞)
Complex Yes
mainCh
two-dimensional vector defining the main channel
frequency limits (as an offset from the single voltage and
current spectral component)
None
(∞:∞)
Real
Yes
None
(∞:∞)
Real
Yes
upperAdjCh two-dimensional vector defining the upper adjacent channel None
frequency limits (as an offset from the single voltage and
current spectral component);
(∞:∞)
Real
Yes
winType
window type
None
†
string
No
winConst
window constant that affects the shape of the applied
window.
0.75
[0:∞)
Real
No
lowerAdjCh the two-dimensional vector defining the lower adjacentchannel frequency limits (as an offset from the single
voltage and current spectral component);
Required
† winType can be: "none", "hamming", "hanning", "gaussian", "kaiser", "8510",
"blackman","blackman-harris"
Examples
VloadFund = vload[1]
IloadFund = iload.i[1]
mainlimits = {-16.4 kHz, 16.4 kHz}
UpChlimits = {mainlimits + 30 kHz}
LoChlimits = {mainlimits - 30 kHz}
TransACPR = acpr_vi(VloadFund, IloadFund, mainlimits, LoChlimits, UpChlimits,
"Kaiser")
where vload is the named connection at a load, and iload.i is the name of the
current probe that samples the current into the node. The {} braces are used to
define vectors, and the upper channel limit and lower channel limit frequencies
do not need to be defined by means of the vector that defines the main channel
limits.
examples/RF_Board/NADC_PA_wrk/NADC_PA_ACPRtransmitted.dds
42
Measurement Expressions
Note
acpr_vi() function is intended to be used in Circuit Envelope design as MeasEqn or in resulting Circuit
Envelope simulation's data display as an Eqn equation. If you want to do similar function in Ptolemy
environment, recommend to look for ACPR/ACLR examples on support website and/or use the
spec_power() function implement similar effect in Ptolemy.
Defined in
$HPEESOF_DIR/expressions/ael/digital_wireless_fun.ael
See Also
acpr_vr() (expmeas), channel_power_vi() (expmeas), channel_power_vr() (expmeas),
relative_noise_bw() (expmeas)
Notes/Equations
Used in Adjacent-channel power computations.
The user must supply a single complex voltage spectral component (for example, the
fundamental) across a load versus time and a single complex current spectral component
into the same load. The user must also supply the upper and lower adjacent-channel and
main-channel frequency limits, as offsets from the spectral component frequency of the
voltage and current. These frequency limits must be entered as two-dimensional vectors.
An optional window and window constant may also be supplied, for use in processing nonperiodic data.
acpr_vr()
Computes the adjacent-channel power ratio following a Circuit Envelope simulation.
Syntax
ACPRvals = acpr_vr(voltage, resistance, mainCh, lowerAdjCh, upperAdjCh, winType,
winConst)
Arguments
43
Measurement Expressions
Name
Description
Default Range Type
voltage
single complex voltage spectral component (for example,
the fundamental) across a load versus time
None
(∞:∞)
Complex Yes
resistance
load resistance in ohms
50
(∞:∞)
Complex No
mainCh
two-dimensional vector defining the main channel
frequency limits (as an offset from the single voltage
spectral component)
None
(∞:∞)
Real
Yes
None
(∞:∞)
Real
Yes
upperAdjCh two-dimensional vector defining the upper adjacent channel None
frequency limits (as an offset from the single voltage
spectral component);
(∞:∞)
Real
Yes
winType
window type
None
†
string
No
winConst
window constant that affects the shape of the applied
window.
0.75
[0:∞)
Real
No
lowerAdjCh the two-dimensional vector defining the lower adjacentchannel frequency limits (as an offset from the single
voltage spectral component);
Required
† winType can be: "none", "hamming", "hanning", "gaussian", "kaiser", "8510",
"blackman","blackman-harris"
Examples
Vfund = vOut[1]
mainlimits = {-(1.2288 MHz/2), (1.2288 MHz/2)}
UpChlimits = {885 kHz, 915 kHz}
LoChlimits = {-915 kHz, -885 kHz}
TransACPR = acpr_vr(VloadFund, 50, mainlimits, LoChlimits, UpChlimits,
"Kaiser")
where vOut is the named connection at a resistive load. The {} braces are used
to define vectors.
Note vOut is a named connection on the schematic. Assuming that a Circuit
Envelope simulation was run, vOut is output to the dataset as a two-dimensional
matrix. The first dimension is time, and there is a value for each time point
in the simulation. The second dimension is frequency, and there is a value for
each fundamental frequency, each harmonic, and each mixing term in the
analysis, as well as the baseband term.
vOut[1] is the equivalent of vOut[::, 1], and specifies all time points at the
lowest non-baseband frequency (the fundamental analysis frequency, unless a
multitone analysis has been run and there are mixing products). For former MDS
users, the notation "vOut[*, 2]" in MDS corresponds to the notation of
"vOut[1]".
examples/Tutorial/ModSources_wrk/IS95RevLinkSrc.dds
Note
acpr_vr() function is intended to be used in Circuit Envelope design as MeasEqn or in resulting Circuit
Envelope simulation's data display as an Eqn equation. If you want to do similar function in Ptolemy
environment, recommend to look for ACPR/ACLR examples on support website and/or use the
spec_power() function implement similar effect in Ptolemy.
Defined in
44
Measurement Expressions
$HPEESOF_DIR/expressions/ael/digital_wireless_fun.ael
See Also
acpr_vi() (expmeas), channel_power_vi() (expmeas), channel_power_vr() (expmeas),
relative_noise_bw() (expmeas)
Notes/Equations
Used in Adjacent-channel power computations.
The user must supply a single complex voltage spectral component (for example, the
fundamental) across a resistive load versus time and the load resistance. The user must
also supply the upper and lower adjacent-channel and main-channel frequency limits, as
offsets from the spectral component frequency of the voltage. These frequency limits must
be entered as two-dimensional vectors. An optional window and window constant may
also be supplied, for use in processing non-periodic data.
channel_power_vi()
Computes the power (in watts) in an arbitrary frequency channel following a Circuit
Envelope simulation.
Syntax
Channel_power = channel_power_vi(voltage, current, mainCh, winType, winConst)
Arguments
Name
Description
Default Range Type
voltage
single complex voltage spectral component (for example, the
fundamental) across a load versus time
None
(∞:∞)
Complex Yes
current
single complex current spectral component into the same load None
versus time
(∞:∞)
Complex Yes
mainCh
two-dimensional vector defining channel frequency limits (as
an offset from the single voltage and current spectral
component †
None
(∞:∞)
Real
Yes
None
†
string
No
[0:∞)
Real
No
winType window type
winConst window constant that affects the shape of the applied window. 0.75
Required
† note that these frequency limits do not have to be centered on the voltage and current
spectral component frequency.
† winType can be: "none", "hamming", "hanning", "gaussian", "kaiser", "8510",
"blackman","blackman-harris"
Examples
VloadFund = vload[1]
IloadFund = iload.i[1]
mainlimits = {-16.4 kHz, 16.4 kHz}
Main_Channel_Power = channel_power_vi(VloadFund, IloadFund, mainlimits,
"Kaiser")
where vload is the named connection at a load, and iload.i is the name of the
45
Measurement Expressions
current probe that samples the current into the node. The {} braces are used to
define a vector. Note that the computed power is in watts. Use the following
equation to convert the power to dBm.
Main_Channel_Power_dBm = 10 * log(Main_Channel_Power) + 30
Do not use the dBm function, which operates on voltages.
examples/RF_Board/NADC_PA_wrk/NADC_PA_ACPRtransmitted.dds
Defined in
$HPEESOF_DIR/expressions/ael/digital_wireless_fun.ael
See Also
acpr_vi() (expmeas), acpr_vr() (expmeas), channel_power_vr() (expmeas)
Notes/Equations
Used in Channel power computations.
The user must supply a single complex voltage spectral component (for example, the
fundamental) across a load versus time, and a single complex current spectral component
into the same load. The user must also supply the channel frequency limits, as offsets
from the spectral component frequency of the voltage and current. These frequency limits
must be entered as a two-dimensional vector. An optional window and window constant
may also be supplied, for use in processing non-periodic data.
channel_power_vr()
Computes the power (in watts) in an arbitrary frequency channel following a Circuit
Envelope simulation.
Syntax
Channel_power = channel_power_vr(voltage, resistance, mainCh, winType, winConst)
Arguments
Name
Description
Default Range Type
voltage
single complex voltage spectral component (for example, the None
fundamental) across a load versus time
Required
(∞:∞)
Complex Yes
resistance load resistance in ohms
50
(∞:∞)
Complex No
mainCh
two-dimensional vector defining the main channel frequency
limits (as an offset from the single voltage spectral
component) †
None
(∞:∞)
Real
Yes
winType
window type
None
††
string
No
0.75
[0:∞)
Real
No
winConst window constant that affects the shape of the applied
window.
† note that these frequency limits do not have to be centered on the voltage and current
spectral component frequency
46
Measurement Expressions
† † winType can be: "none", "hamming", "hanning", "gaussian", "kaiser", "8510",
"blackman","blackman-harris"
Examples
Vmain_fund = Vmain[1]
mainlimits = {-16.4 kHz, 16.4 kHz}
Main_Channel_Power = channel_power_vr(Vmain_fund, 50, mainlimits, "Kaiser")
where Vmain is the named connection at a resistive load (50 ohms in this case.)
The {} braces are used to define a vector. Note that the computed power is in
watts. Use the equation
Main_Channel_Power_dBm = 10 * log(Main_Channel_Power) + 30
to convert the power to dBm. Do not use the dBm function, which operates on
voltages.
Example file
examples/RF_Board/NADC_PA_wrk/NADC_PA_ACPRreceived.dds
Defined in
$HPEESOF_DIR/expressions/ael/digital_wireless_fun.ael
See Also
acpr_vi() (expmeas), acpr_vr() (expmeas), channel_power_vi() (expmeas)
Notes/Equations
Used in Channel power computations.
The user must supply a single complex voltage spectral component (for example, the
fundamental) across a load versus time and the resistance of the load. The user must also
supply the channel frequency limits, as offsets from the spectral component frequency of
the voltage. These frequency limits must be entered as a two-dimensional vector. An
optional window and window constant may also be supplied, for use in processing nonperiodic data.
const_evm()
Takes the results of a Circuit Envelope simulation and generates data for the ideal and
distorted constellation and trajectory diagrams, as well as the error vector magnitude, in
percent, and a plot of the error vector magnitude versus time.
Syntax
data = const_evm(vfund_ideal, vfund_dist, symbol_rate, sampling_delay, rotation,
transient_duration, path_delay)
Arguments
47
Measurement Expressions
Name
Description
Default Range Type
vfund_ideal
single complex voltage spectral component (for
example the fundamental) that is ideal
(undistorted). This could be constructed from two
baseband signals instead, by using the function
cmplx().
None
(∞:∞)
Complex Yes
vfund_dist
single complex voltage spectral component (for
example, the fundamental) that has been distorted
by the network being simulated. This could be
constructed from two baseband signals instead, by
using the function cmplx()
None
(∞:∞)
Complex Yes
symbol_rate
symbol rate of the modulation signal
None
[0:∞)
Integer,
real
Yes
sampling_delay
sampling delay †
0
[0:∞)
Integer,
real
No
rotation
parameter that rotates the constellations by that
many radian ††
0
[0:∞)
Integer,
real
No
transient_duration time in seconds that causes this time duration of
symbols to be eliminated from the error-vectormagnitude calculation †† †
0
[0:∞)
Integer,
real
No
time in seconds of the sum of all delays in the signal 0
path †† ††
[0:∞)
Integer,
real
No
path_delay
Required
† sampling_delay - (if nonzero) throws away the first delay = N seconds of data from the
constellation and trajectory plots. It is also used to interpolate between simulation time
points, which is necessary if the optimal symbol-sampling instant is not exactly at a
simulation time point. Usually this parameter must be nonzero to generate a constellation
diagram with the smallest grouping of sample points
†† rotation does not need to be entered, and it will not affect the error-vector-magnitude
calculation, because both the ideal and distorted constellations will be rotated by the same
amount.
†† † Usually the filters in the simulation have transient responses, and the error-vectormagnitude calculation should not start until these transient responses have finished.
†† †† If the delay is 0, this parameter may be omitted. If it is non-zero, enter the delay
value. This can be calculated by using the function delay_path().
Examples
rotation = -0.21
sampling_delay = 1/sym_rate[0, 0] - 0.5 * tstep[0, 0]
vfund_ideal = vOut_ideal[1]
vfund_dist = vOut_dist[1]
symbol_rate = sym_rate[0, 0]
data = const_evm(vfund_ideal, vfund_dist, symbol_rate, sampling_delay,
rotation, 1.5ms, path_delay)
where the parameter sampling_delay can be a numeric value, or in this case an
equation using sym_rate, the symbol rate of the modulated signal, and tstep,
the time step of the simulation. If these equations are to be used in a Data
Display window, sym_rate and tstep must be defined by means of a variable (VAR)
component, and they must be passed into the dataset as follows: Make the
parameter Other visible on the Envelope simulation component, and edit it so
that
Other = OutVar = sym_rate OutVar = tstep
In some cases, it may be necessary to experiment with the delay value to get
the constellation diagrams with the tightest points.
48
Measurement Expressions
Note that const_evm() returns a list of data. So in the example above,
data[0]= ideal constellation
data[1]= ideal trajectory
data[2]= distorted constellation
data[3]= distorted trajectory
data[4]= error vector magnitude versus time
data[5]= percent error vector magnitude
Refer to the example file to see how these data are plotted.
Defined in
$HPEESOF_DIR/expressions/ael/digital_wireless_fun.ael
See Also
constellation() (expmeas), delay_path() (expmeas), sample_delay_pi4dqpsk() (expmeas),
sample_delay_qpsk() (expmeas)
Notes/Equations
Used in constellation and trajectory diagram generation and error-vector-magnitude
calculation.
The user must supply a single complex voltage spectral component (for example, the
fundamental) that is ideal (undistorted), as well as a single complex voltage spectral
component (for example, the fundamental) that has been distorted by the network being
simulated. These ideal and distorted complex voltage waveforms could be generated from
baseband I and Q data. The user must also supply the symbol rate, a delay parameter, a
rotation factor, and a parameter to eliminate any turn-on transient from the error-vectormagnitude calculation are optional parameters.
The error vector magnitude is computed after correcting for the average phase difference
and RMS amplitude difference between the ideal and distorted constellations.
cross_hist()
Returns jitter histogram
Syntax
y = cross_hist(Vout_time, time_start, time_stop, level_low, level_high, number_of_bins,
BitRate, No_of_Eye, Delay, steps)
Arguments
49
Measurement Expressions
Name
Description
Default Range Type
Required
Vout_time
time domain voltage waveform
None
(∞:∞)
Real
Yes
time_start
define the rectangular window points for jitter histogram None
plot
[0:∞)
Real
Yes
time_stop
define the rectangular window points for jitter histogram None
plot
[0:∞)
Real
Yes
level_low
define the rectangular window points for jitter histogram None
plot
[0:∞)
Real
Yes
level_high
define the rectangular window points for jitter histogram None
plot
[0:∞)
Real
Yes
number_of_bins defines the number of bins on the time axis of eye
diagram and controls the resolution of jitter histogram
plot
None
[1:∞)
Integer Yes
BitRate
bit rate of the channel and is expressed in frequency
units
None
(0:∞)
Real
No_of_Eye
Used for multiple eye jitter histogram plots
None
[0:∞)
Integer Yes
Delay
used to remove initial transient in the eye diagram and
is expressed in time units
None
[0:∞)
Real
steps
represents the number of sampling points between
level_low and level_high and is used for controlling the
density of jitter histogram.
None
[1:∞)
Integer Yes
Yes
Yes
Examples
Jitter_Histogram = cross_hist(vout, 0 ps, 100 ps, 0 V, 0.1V, 300, 10 GHz, 1,0,
20)
Defined in
Built in
See Also
eye_amplitude() (expmeas), eye_closure() (expmeas), eye_fall_time() (expmeas),
eye_rise_time() (expmeas), eye_height() (expmeas)
Notes/Equations
Jitter histogram plots the jitter histogram of a time domain voltage waveform.
delay_path()
This function is used to determine the time delay and the constellation rotation angle
between two nodal points along a signal path.
Syntax
y = delay_path(vin, vout)
Arguments
50
Measurement Expressions
Name Description
Default Range Type
Required
vin
envelope (I + j * Q) at the input
node
None
(∞:∞)
Complex Yes
vout
I + j * Q at the output node
None
(∞:∞)
Complex Yes
Examples
x = delay_path(vin[1], vout[1])
where vin[1] and vout[1] are complex envelopes around the first carrier
frequency in envelope simulation. In return, x[0] is the time delay (in
seconds) between vin and vout. x[1] is the rotation angle (in radians) between
vin and vout constellations.
or
x = delay_path(T1, T2)
where T1 and T2 are instance names of two TimedSink components.
Defined in
Built in
See Also
ber_pi4dqpsk() (expmeas), ber_qpsk() (expmeas), const_evm() (expmeas), cross_corr()
(expmeas)
Notes/Equations
Used in Circuit Envelope simulation, Ptolemy simulation.
This function outputs an array of two values. The first value, data[0], is the time delay
between vin and vout. The second value, data[1], is the rotation angle between vinconstellation and vout-constellation.
Note
This function is only available in 32-bit simulator.
evm_wlan_dsss_cck_pbcc()
Returns EVM (error vector magnitude) analysis results for WLAN DSSS/CCK/PBCC (IEEE
802.11b and IEEE 802.11g non-OFDM) voltage signals.
Syntax
evm = evm_wlan_dsss_cck_pbcc(voltage{, mirrorSpectrum, start, averageType,
burstsToAverage, modulationFormat, searchTime, resultLengthType, resultLength,
measurementOffset, measurementInterval, chipRate, clockAdjust, equalizationFilter,
filterLength, descrambleMode, referenceFilter, referenceFilterBT, output})
Arguments
51
Measurement Expressions
Name
Description
Default
Range
Type
voltage
complex envelope
WLAN
DSSS/CCK/PBCC
voltage signal
None
(-∞:∞)
Complex Yes
mirrorSpectrum
specifies whether the NO
input signal should be
mirrored or not
See Notes
String
start
specifies the start
time for the EVM
analysis
[0:max(indep(voltage))] Real
No
averageType
specifies what type of OFF
averaging is done
See Notes
String
No
burstsToAverage
number of bursts over 20
which the results will
be averaged
(0:∞)
Integer
No
modulationFormat
modulation format
"Auto Detect"
See Notes
String
No
searchTime
search time
550 usec
[0:max(indep(voltage))] Real
No
resultLengthType
specifies how the
result length is
determined
"Auto Select"
See Notes
String
No
resultLength
result length in chips
2816
[1:108344]
Integer
No
measurementOffset
measurement offset in 22
chips
(0:∞)
Integer
No
measurementInterval measurement interval 2794
in chips
(0:∞)
Integer
No
chipRate
chip rate in Hz
(0:∞)
Real
No
clockAdjust
clock adjustment as a 0
fraction of a chip
[-0.5, 0.5]
Real
No
equalizationFilter
specifies whether an
equalization filter is
used or not
OFF
See Notes
String
No
filterLength
equalization filter
length in chips
21
[3:∞) must be odd
Integer
No
descrambleMode
specifies how
descrambling is done
On
See Notes
String
No
referenceFilter
specifies the reference Gaussian
filter to be used
See Notes
String
No
referenceFilterBT
BT value for the
reference filter if a
Gaussian reference
filter is selected
[0.05:100]
Real
No
output
EVM analysis result to Avg_EVMrms_pct See Notes
be returned
String
No
first point of the
input data
11e6 Hz
0.3
Required
No
Examples
evmRMS = evm_wlan_dsss_cck_pbcc(Vout[1])
where Vout is a named node in a Circuit Envelope simulation, will return the
EVM rms value in percent for the voltage envelope at the fundamental frequency.
The voltage data Vout[1] must contain at least one complete burst. The EVM
result will be from the analysis of the first burst in the input signal.
evmPk = evm_wlan_dsss_cck_pbcc(Vout[1], , , "RMS (Video)", 10, , 300e-6, , , ,
, , , , , , "Gaussian", 0.5, "EVM_Pk_pct")
where Vout is a named node in a Circuit Envelope simulation, will return a
52
Measurement Expressions
vector with 10 values each representing the peak EVM in percent for the first
10 bursts in the voltage envelope at the fundamental frequency. Since
searchTime is set to 300 usec, the first 300 usec of Vout[1] must contain at
least one complete burst. In addition, since 10 bursts need to be processed,
Vout[1] must contain at least 10 complete bursts. A Gaussian filter with BT=0.5
will be used as a reference filter.
AvgMagErr = evm_wlan_dsss_cck_pbcc(Vout[1], , , "RMS (Video)", 3, , 400e-6, , ,
100, 500, , , , , , , , "Avg_MagErr_rms_pct")
where Vout is a named node in a Circuit Envelope simulation, will return the
average (over 3 bursts) magnitude error in percent for the voltage envelope at
the fundamental frequency. Since searchTime is set to 400 usec, the first 400
usec of Vout[1] must contain at least one complete burst. In addition, since 3
bursts need to be averaged, Vout[1] must contain at least 3 complete bursts.
Only the chips 101 to 600 (measurementOffset = 100 and measurementInterval =
500) will be considered for the EVM analysis.
Defined in
Built in
See Also
evm_wlan_ofdm() (expmeas)
Notes/Equations
Used in Circuit Envelope simulation and Data Flow simulation.
This expression can be used with input data of up to two dimensions. Only complex
envelope input signals are allowed as input.
The evm_wlan_dsss_cck_pbcc() expression performs an EVM measurement for WLAN
DSSS/CCK/PBCC (IEEE 802.11b and IEEE 802.11g non-OFDM) signals. Available
Measurement Results for evm_wlan_dsss_cck_pbcc() displays the available measurement
results.
Available Measurement Results for evm_wlan_dsss_cck_pbcc()
53
Measurement Expressions
Measurement Result
Description
Avg_WLAN_80211b_1000_chip_Pk_EVM_pct average EVM in percentage as specified by the standard (section
18.4.7.8 Transmit modulation accuracy in 802.11b specification;
pages 55-57) except that the EVM value is normalized
WLAN_80211b_1000_chip_Pk_EVM_pct
EVM in percentage as specified by the standard (section
18.4.7.8 Transmit modulation accuracy in 802.11b specification;
pages 55-57) with the exception that the EVM value is
normalized versus burst
Avg_EVMrms_pct
average EVM rms in percentage as defined in the Agilent 89600
VSA
EVMrms_pct
EVM rms in percentage as defined in the Agilent 89600 VSA
versus burst
EVM_Pk_pct
peak EVM in percentage versus burst
EVM_Pk_chip_idx
peak EVM chip index versus burst
Avg_MagErr_rms_pct
average magnitude error rms in percentage
MagErr_rms_pct
magnitude error rms in percentage versus burst
MagErr_Pk_pct
peak magnitude error in percentage versus burst
MagErr_Pk_chip_idx
peak magnitude error chip index versus burst
Avg_PhaseErr_deg
average phase error in degrees
PhaseErr_deg
phase error in degrees versus burst
PhaseErr_Pk_deg
peak phase error in degrees versus burst
PhaseErr_Pk_chip_idx
peak phase error chip index versus burst
Avg_FreqError_Hz
average frequency error in Hz
FreqError_Hz
frequency error in Hz versus burst
Avg_IQ_Offset_dB
average IQ offset in dB
IQ_Offset_dB
IQ offset in dB versus burst
Avg_SyncCorrelation
average sync correlation
SyncCorrelation
sync correlation versus burst
Results whose name is prefixed with " Avg"_ are averaged over the number of bursts
specified by the user (if averageType is set to " RMS ( Video )"). Results whose name is
not prefixed with " Avg"_ are results versus burst.
The following is a brief description of the algorithm used (the algorithm used is the same
as the one used in the Agilent 89600 VSA) and a detailed description of its arguments.
Starting at the time instant specified by the start argument, a signal segment of length
searchTime is acquired. This signal segment is searched in order for a complete burst to
be detected. The burst search algorithm looks for both a burst on and a burst off
transition. In order for the burst search algorithm to detect a burst, an idle part must exist
between consecutive bursts and the bursts must be at least 15 dB above the noise floor.
If the acquired signal segment does not contain a complete burst, the algorithm will not
detect any burst and the analysis that follows will most likely produce wrong results.
Therefore, searchTime must be long enough to acquire at least one complete burst. Since
the time instant specified by the start argument can be a little after the beginning of a
burst, it is recommended that searchTime is set to a value approximately equal to 2 x
burstLength, where burstLength is the duration of a burst in seconds including the
duration of the idle part. If it is known that the time instant specified by the start
argument is a little before the beginning of a burst, then searchTime can be set to
burstLength.
After a burst is detected, synchronization is performed based on the preamble. The burst
54
Measurement Expressions
is then demodulated. Finally, the burst is analyzed to get the EVM measurement results.
If averageType is set to OFF , only one burst is detected, demodulated, and analyzed.
If averageType is set to RMS (Video) , after the first burst is analyzed the signal segment
corresponding to it is discarded and new signal samples are acquired to fill in the signal
buffer of length searchTime. When the buffer is full again a new burst search is performed
and when a burst is detected it is demodulated and analyzed. These steps repeat until
burstsToAverage bursts are processed.
If for any reason a burst is misdetected the results from its analysis are discarded. The
EVM results obtained from all the successfully detected, demodulated, and analyzed bursts
are averaged to give the final result.
The mirrorSpectrum argument accepts the following strings: "NO" and "YES". This
argument can be used to mirror (conjugate) the input signal before any other processing
is done. Mirroring the input signal is necessary if the configuration of the mixers in your
system has resulted in a mirrored signal compared to the one at the input of the upconverter and if the preamble and header are short format. In this case, if mirrorSpectrum
is not set to " YES " the header bits (which carry the modulation format and length
information) will not be recovered correctly so the demodulation of the PSDU part of the
burst will most likely fail.
The start argument sets the starting point for acquiring the signal to be processed. By
default, the starting point is the beginning of the input signal (voltage argument).
However, if for any reason an initial part of the input signal needs to be omitted this can
be done by setting the start argument appropriately.
The averageType argument accepts the following strings: "Off" and "RMS (Video)". This
argument can be used to turn on/off video averaging. If set to "Off" the EVM result
returned is from the processing of only one burst. Otherwise, multiple bursts are
processed and the results are averaged.
The burstsToAverage argument set the number of bursts whose results will be averaged if
averageType is set to "RMS (Video)". If averageType is set to "Off" this argument is
ignored.
The modulationFormat argument accepts the following strings: "Auto Detect", "Barker 1",
"Barker 2", "CCK 5.5", "CCK 11", "PBCC 5.5", "PBCC 11", "PBCC 22", "PBCC 33". This
argument sets the modulation format used in the PSDU part of the burst. If
modulationFormat is set to "Auto Detect", the algorithm will use the information detected
in the PLCP header part of the burst to automatically determine the modulation format.
Otherwise, the modulation format determined from the PLCP header is ignored and the
modulation format specified by the modulationFormat argument is used in the
demodulation of the PSDU part of the burst.
The searchTime argument sets the duration of the signal segment that is acquired and
searched in order to detect a complete burst. Recommendations on how to set this
argument are given in the brief description of the algorithm used by this expression earlier
in these Notes/Equations section.
The resultLengthType argument accepts the following strings: "Auto Select" and "Manual
Override". The resultLengthType and resultLength arguments control how much data is
acquired and demodulated.
When resultLengthType is set to " Auto Select", the measurement result length is
55
Measurement Expressions
automatically determined from the information in the PLCP header part of the burst.
In this case, the argument resultLength defines a maximum result length for the
burst in symbol times; that is, if the measurement result length that is automatically
detected is bigger than resultLength it will be truncated to resultLength. The
maximum result length specified by the resultLength argument includes the PLCP
preamble and PLCP header.
When resultLengthType is set to " Manual Override ", the measurement result length
is set to resultLength regardless of what is detected in the PLCP header part of the
burst. The result length specified by the resultLength argument includes the PLCP
preamble and PLCP header.
Measurement result length setting summarizes the differences between how "Auto Select"
and " Manual Override " modes determine the measurement result length. The table lists
the measurement result lengths actually used for " Auto Select" and " Manual Override"
modes for three different values of the resultLength argument (3300, 2816 and 2200
chips). It is assumed that the input burst is 2816 symbols long.
Measurement result length setting
resultLengthType resultLength Measurement Result Length Actually Used
Auto Select
2200
2200
Auto Select
2816
2816
Auto Select
3300
2816
Manual Override
2200
2200
Manual Override
2816
2816
Manual Override
3300
3300
Note that when resultLengthType is set to " Manual Override" and resultLength=3300
(greater than the actual burst size) the algorithm will demodulate the full 3300 chips even
though this is 484 chips beyond the burst width.
The measurementOffset and measurementInterval arguments can be used to isolate a
specific segment of the burst for analysis. The values of measurementInterval and
measurementOffset are in number of chips and are relative to the ideal starting point of
the PLCP preamble portion of the burst. For a signal that uses the long PLCP format, the
ideal starting point of the PLCP preamble is exactly 128 symbol times (128 x 11 chips)
before the start of the SFD sync pattern. For a signal that uses the short PLCP format, the
ideal starting point of the PLCP preamble is exactly 56 symbol times (56 x 11 chips)
before the start of the SFD sync pattern.
The chipRate argument sets the fundamental chip rate of the signal to be analyzed. The
default is 11 MHz, which matches the chip rate of 802.11b and 802.11g; however, this
argument can be used when experimenting with signals that do not follow the standard
specifications. A special case is the optional 802.11g 33 Mbit PBCC mode, where the chip
rate of the transmitted signal starts at 11 MHz, but changes to 16.5 MHz in the middle of
the burst. In this case chipRate should still be set to 11 MHz (the algorithm will
automatically switch to 16.5 MHz at the appropriate place in the burst).
Although the algorithm synchronizes to the chip timing of the signal, it is possible for the
synchronization to be slightly off. The clockAdjust argument allows the user to specify a
timing offset which is added to the chip timing detected by the algorithm. This argument
should only be used when trying to debug unusual signals.
The equalizationFilter argument accepts the following strings: "OFF" and "ON". This
argument can be used to turn on/off the equalization filter. The filterLength argument sets
56
Measurement Expressions
the equalization filter length (in number of chips). Using an equalization filter can
dramatically improve the EVM results since the equalizer can compensate for ISI due to
the transmit filter. However, it can also compensate the distortion introduced by the DUT.
If the filter used in the transmitter is Gaussian, then having the equalizer off and selecting
a Gaussian reference filter might be a better option.
The descrambleMode argument accepts the following strings: "Off", "Preamble Only",
"Preamble & Header Only", "On". This argument can be used to control how descrambling
is done.
"Off" does no descrambling.
"Preamble Only" descrambles only the PLCP preamble.
"Preamble & Header Only" descrambles only the PLCP preamble and PLCP header.
"On" descrambles all parts of the burst.
Normally, 802.11b or 802.11g signals have all bits scrambled before transmission, so
this parameter should normally be set to "On" . However, when debugging an
802.11b or 802.11g transmitter, it is sometimes helpful to disable scrambling in the
transmitter, in which case you should disable descrambling in this component.
If the input signal's preamble is scrambled but you disable descrambling of the preamble
(or vice versa), then the algorithm will not be able to synchronize to the signal properly.
Similarly, if the input signal's header is scrambled but you disable descrambling of the
header (or vice versa) then the algorithm will not be able to correctly identify the burst
modulation type and burst length from the header.
The referenceFilter argument accepts the following strings: "Rectangular" and "Gaussian".
This argument can be used to select a reference filter for the EVM analysis. Although, the
IEEE 802.11b/g standards do not specify either a transmit filter or a receive filter, they do
have a spectral mask requirement, and a transmitter must use some sort of transmit filter
to meet the spectral mask. On the other hand, the description of the EVM measurement in
the standard does not use any receive or measurement filter. The absence of the need to
use any transmit or receive filter is partly because the standard has a very loose limit for
EVM (35% peak on 1000 chips worth of data).
If the standard definition is followed when computing EVM, no measurement or reference
filter should be used (referenceFilter must be set to "Rectangular"). However, what this
means is that even a completely distortion-free input signal will still give non-zero EVM
unless the input signal has a zero-ISI transmit filter. If a non-zero-ISI transmit filter is
used and there is additional distortion added to the signal due to the DUT, then the EVM
will measure the overall error due to both the transmit filter's ISI and the DUT distortion.
Turning on the equalizer will remove most of the transmit filter's ISI but it can also
remove some of the distortion introduced by the DUT. To get a better idea of the EVM due
to the DUT distortion a reference filter that matches the transmit filter can be used.
Currently, only "Rectangular" and "Gaussian" filters are available as reference filters.
The referenceFilterBT argument sets the BT (Bandwidth Time product) for the Gaussian
reference filter. If referenceFilter is set to "Rectangular" this argument is ignored.
The output argument accepts the following strings (see Available Measurement Results for
evm_wlan_dsss_cck_pbcc()): "Avg_WLAN_80211b_1000_chip_Pk_EVM_pct",
"WLAN_80211b_1000_chip_Pk_EVM_pct", "Avg_EVMrms_pct", "EVMrms_pct",
"EVM_Pk_pct", "EVM_Pk_chip_idx", "Avg_MagErr_rms_pct", "MagErr_rms_pct",
"MagErr_Pk_pct", "MagErr_Pk_chip_idx". "Avg_PhaseErr_deg", "PhaseErr_deg",
57
Measurement Expressions
"PhaseErr_Pk_deg", "PhaseErr_Pk_chip_idx", "Avg_FreqError_Hz", "FreqError_Hz",
"Avg_IQ_Offset_dB", "IQ_Offset_dB", "Avg_SyncCorrelation", "SyncCorrelation". This
argument selects which EVM analysis result will be returned.
Relationship Between WLAN_802_11b Source Parameters and evm_wlan_dsss_cck_pbcc()
Expression Arguments summarizes how some of the arguments of the
evm_wlan_dsss_cck_pbcc() expression should be set based on the parameter values of
the WLAN_802_11b source.
Relationship Between WLAN_802_11b Source Parameters and evm_wlan_dsss_cck_pbcc() Expression Arguments
WLAN_802_11b
evm_wlan_dsss_cck_pbcc() Comments
DataRate (default
is 11 Mbps)
searchTime (default is 550
µsec)
The recommended searchTime is !expmeas-05-0901.gif! . BurstLength=
tRamp+tPLCP+tPSDU+IdleInterval, where, tRamp =
!expmeas-05-09-02.gif! tPLCP = !expmeas-05-0903.gif! tPSDU = !expmeas-05-09-04.gif!
MirrorSpectrum
(default is NO)
mirrorSpectrum (default is NO)
If DUT introduces spectrum mirroring, then
mirrorSpectrum must be set to "NO" ("YES") when
MirrorSpectrum is set to "YES" ("NO"); otherwise
mirrorSpectrum must be set to the same value as
MirrorSpectrum.
FilterType (default
is Gaussian)
referenceFilter (default is
Gaussian)
When FilterType is set to "Gaussian", the recommended
setting of referenceFilter is "Gaussian"; otherwise, the
recommended setting is "Rectangular"
GaussianFilter_bT
(default is 0.3)
referenceFilterBT (default is
0.3)
The recommended setting of referenceFilterBT is the
same value as GaussianFilter_bT. This parameter is
only used when referenceFilter is set to "Gaussian".
PreambleFormat
(default is Long)
PwrRamp (default
is None)
IdleInterval
(default is 10 µsec)
DataLength
(default is 100)
Note
This function is only available in 32-bit simulator.
evm_wlan_ofdm()
Returns EVM (error vector magnitude) analysis results for WLAN OFDM (IEEE 802.11a)
voltage signals
Syntax
evm = evm_wlan_ofdm(voltage{, mirrorSpectrum, start, averageType, burstsToAverage,
subcarrierModulation, guardInterval, searchTime, resultLengthType, resultLength,
measurementOffset, measurementInterval, subcarrierSpacing, symbolTimingAdjust, sync,
output})
Arguments
58
Measurement Expressions
Name
Description
Default
Range
Type
Required
voltage
complex envelope
WLAN OFDM
(orthogonal frequency
division multiplexing)
voltage signal
None
(-∞:∞)
Complex Yes
mirrorSpectrum
specifies whether the
input signal should be
mirrored or not
NO
See Notes
String
start
specifies the start time first point of the
for the EVM analysis
input data
[0:max(indep(voltage))] Real
No
averageType
specifies what type of
averaging is done
OFF
See Notes
String
No
burstsToAverage
number of bursts over
which the results will
be averaged
20
(0:∞)
Integer
No
subcarrierModulation data subcarrier
modulation format
"Auto Detect"
See Notes
String
No
guardInterval
guard interval length
for the OFDM symbols
(as a fraction of the
FFT time period)
0.25
[0:1]
Real
No
searchTime
search time
80 usec
[0:max(indep(voltage))] Real
No
resultLengthType
specifies how the result "Auto Select"
length is determined
See Notes
String
No
resultLength
result length in OFDM
symbols
60
[1:1367]
Integer
No
measurementOffset
measurement offset in
OFDM symbols
0
[0:∞)
Integer
No
measurementInterval measurement interval
in OFDM symbols
11
(0:∞)
Integer
No
subcarrierSpacing
frequency spacing
between the
subcarriers
312.5 kH
(0:∞)
Real
No
symbolTimingAdjust
specifies (as a percent -3.125
of the FFT time period)
the timing adjustment
done on the OFDM
symbols before
performing the FFT
[-100*guardInterval:0]
Real
No
sync
preamble sequence
that will be used for
synchronization
Short Training
Seq
See Notes
String
No
output
EVM analysis result to
be returned
EVMrms_percent See Notes
String
No
No
Examples
evmRMS = evm_wlan_ofdm(Vout[1])
where Vout is a named node in a Circuit Envelope simulation, will return the
evm rms value in percent for the voltage envelope at the fundamental frequency.
The voltage data Vout[1] must contain at least one complete OFDM burst.
iqOffset = evm_wlan_ofdm( Vout[1], , , "RMS (Video)", 5, , 0.125, 200e-6, , ,
5, 10, , , , "IQ_Offset_dB")
where Vout is a named node in a Circuit Envelope simulation, will return the IQ
offset in dB for the voltage envelope at the fundamental frequency. Five bursts
59
Measurement Expressions
will be analyzed and their results averaged. The guard interval used in the
generation of the input signal must be 0.125. Since searchTime is set to 200
usec, the first 200 usec of Vout[1] must contain at least one complete OFDM
burst. In addition, since 5 bursts need to be averaged Vout[1] must contain at
least 5 complete OFDM bursts. Only the OFDM symbols 6 to 15 (measurementOffset
= 5 and measurementInterval = 10) will be considered for the EVM analysis.
Defined in
Built in
See Also
evm_wlan_dsss_cck_pbcc() (expmeas)
Notes/Equations
Used in Circuit Envelope simulation and Data Flow simulation.
This expression can be used with input data of up to two dimensions. Only complex
envelope input signals are allowed as input.
The evm_wlan_ofdm() expression performs an EVM measurement for WLAN OFDM (IEEE
802.11a) signals. Available Measurement Results for evm_wlan_ofdm() seen below,
displays the available measurement results.
Available Measurement Results for evm_wlan_ofdm()
Measurement Result Description
EVMrms_percent
average EVM rms in percentage
EVM_dB
average EVM in dB
PilotEVM_dB
average pilot EVM in dB
CPErms_percent
average Common Pilot Error rms in percentage
IQ_Offset_dB
average IQ offset in dB
SyncCorrelation
average sync correlation
The following is a brief description of the algorithm used (the algorithm used is the same
as the one used in the Agilent 89600 VSA) and a detailed description of its arguments.
Structure of an OFDM burst. shows the structure of an OFDM burst. Many of the terms
mentioned later in these notes such as the preamble, SIGNAL symbol, DATA symbols,
guard intervals (GI) are shown in this figure.
60
Measurement Expressions
Structure of an OFDM burst.
Starting at the time instant specified by the start argument, a signal segment of length
searchTime is acquired. This signal segment is searched in order for a complete burst to
be detected. The burst search algorithm looks for both a burst on and a burst off
transition. In order for the burst search algorithm to detect a burst, an idle part must exist
between consecutive bursts and the bursts must be at least 15 dB above the noise floor.
If the acquired signal segment does not contain a complete burst, the algorithm will not
detect any burst and the analysis that follows will most likely produce incorrect results.
Therefore, searchTime must be long enough to acquire at least one complete burst. Since
the time instant specified by the start argument can be a little after the beginning of a
burst, it is recommended that searchTime is set to a value approximately equal to 2 x
burstLength, where burstLength is the duration of a burst in seconds including the
duration of the idle part. If it is known that the time instant specified by the start
argument is a little before the beginning of a burst, then searchTime can be set to
burstLength.
After a burst is detected, synchronization is performed based on the value of the sync
argument. The burst is then demodulated. Finally, the burst is analyzed to get the EVM
measurement results.
If averageType is set to Off , only one burst is detected, demodulated, and analyzed.
If averageType is set to RMS (Video) , after the first burst is analyzed the signal segment
corresponding to it is discarded and new signal samples are acquired to fill in the signal
buffer of length searchTime. When the buffer is full again a new burst search is performed
and when a burst is detected it is demodulated and analyzed. These steps repeat until
burstsToAverage bursts are processed.
If for any reason a burst is mis-detected, the results from its analysis are discarded. The
EVM results obtained from all the successfully detected, demodulated, and analyzed bursts
are averaged to give the final result.
The mirrorSpectrum argument accepts the following strings: "NO" and "YES". This
argument can be used to mirror (conjugate) the input signal before any other processing
is done. Mirroring the input signal is necessary if the configuration of the mixers in your
system has resulted in a mirrored signal compared to the one at the input of the up61
Measurement Expressions
converter. The demodulation process recovers a lot of the information about the burst
from the burst preamble and SIGNAL symbol. If the input signal is mirrored, then some of
this information may not be recovered correctly and the demodulation will most likely fail.
The start argument sets the starting point for acquiring the signal to be processed. By
default, the starting point is the beginning of the input signal (voltage argument).
However, if for any reason an initial part of the input signal needs to be omitted this can
be done by setting the start argument appropriately.
The averageType argument accepts the following strings: "Off" and "RMS (Video)". This
argument can be used to turn on/off video averaging. If set to "Off" the EVM result
returned is from the processing of only one burst. Otherwise, multiple bursts are
processed and the results are averaged.
The burstsToAverage argument set the number of bursts whose results will be averaged if
averageType is set to "RMS (Video)". If averageType is set to "Off" this argument is
ignored.
The subcarrierModulation argument accepts the following strings: "Auto Detect", "BPSK",
"QPSK", "QAM 16", and "QAM 64". This argument sets the data subcarrier modulation
format. If subcarrierModulation is set to " Auto Detect" , the algorithm will use the
information detected within the OFDM burst (SIGNAL symbol - RATE data field) to
automatically determine the data subcarrier modulation format. Otherwise, the format
determined from the OFDM burst will be ignored and the format specified by the
subcarrierModulation argument will be used in the demodulation for all data subcarriers.
This argument has no effect on the demodulation of the pilot subcarriers and the SIGNAL
symbol, whose format is always BPSK.
The guardInterval argument sets the guard interval (also called cyclic extension) length
for the OFDM symbols. The value is expressed as a fraction of the FFT time period and so
its valid range is [0, 1]. The value must match the guard interval length actually used in
the generation of the input signal in order for the demodulation to work properly.
The searchTime argument sets the duration of the signal segment that is acquired and
searched in order to detect a complete OFDM burst. Recommendations on how to set this
argument are given in the brief description of the algorithm used by this expression earlier
in these Notes/Equations section.
The resultLengthType argument accepts the following strings: "Auto Select" and "Manual
Override". The resultLengthType and resultLength arguments control how much data is
acquired and demodulated.
When resultLengthType is set to " Auto Select", the measurement result length is
automatically determined from the information in the decoded SIGNAL symbol
(LENGTH data field). In this case, the argument resultLength defines a maximum
result length for the burst in symbol times; that is, if the measurement result length
that is automatically detected is bigger than resultLength it will be truncated to
resultLength.
When resultLengthType is set to " Manual Override ", the measurement result length
is set to resultLength regardless of what is detected from the SIGNAL symbol of the
burst. The value specified in resultLength includes the SIGNAL symbol but does not
include any part of the burst preamble.
62
Measurement Expressions
Measurement Result Length Setting table shown below, summarizes the differences
between how "Auto Select" and " Manual Override " modes determine the measurement
result length. The table lists the measurement result lengths actually used for "Auto
Select" and " Manual Override" modes for three different values of the resultLength
argument (30, 26 and 20 symbols). It is assumed that the input burst is 26 symbols long.
Measurement Result Length Setting
resultLengthType resultLength Measurement Result Length Actually Used
Auto Select
20
20
Auto Select
26
26
Auto Select
30
26
Manual Override
20
20
Manual Override
26
26
Manual Override
30
30
Note that when resultLengthType is set to " Manual Override" and resultLength=30
(greater than the actual burst size) the algorithm will demodulate the full 30 symbols even
though this is 4 symbols beyond the burst width.
The measurementOffset and measurementInterval arguments can be used to isolate a
specific segment of the burst for analysis. Both are expressed in number of OFDM
symbols. The offset starts counting from the SIGNAL symbol. An offset of 0 will include
the SIGNAL symbol in the EVM analysis, an offset of 1 will exclude the SIGNAL symbol,
and an offset of 5 will exclude the SIGNAL symbol as well as the first 4 DATA symbols.
Interrelationship between searchTime, resultLength, measurementInterval, and
measurementOffsetnshown below illustrates the interrelationship between searchTime,
resultLength, measurementInterval, and measurementOffset.
63
Measurement Expressions
Interrelationship between searchTime, resultLength, measurementInterval, and measurementOffset.
The subcarrierSpacing argument sets the frequency spacing between the subcarriers of
the OFDM signal. The value must match the subcarrier spacing actually used in the
generation of the input signal in order for the demodulation to work properly.
The symbolTimingAdjust argument sets the timing adjustment done on the OFDM symbols
before performing the FFT. The value is expressed as a percent of the FFT time period. Its
valid range is [-100*guardInterval, 0]. Normally, when demodulating an OFDM symbol,
the guard interval is skipped and an FFT is performed on the last portion of the symbol.
However, this means that the FFT will include the transition region between this symbol
and the following symbol. To avoid this, it is generally beneficial to back away from the
end of the symbol and use part of the guard interval. The symbolTimingAdjust argument
controls how far the FFT part of the symbol is adjusted away from the end of the symbol.
Note that the value of this argument is negative because the FFT start time is moved back
by the amount specified by it. The definition of symbolTimingAdjust shown below, explains
this concept graphically. When setting this argument, care should be taken to not back
away from the end of the symbol too much because this may make the FFT include
corrupt data from the transition region at the beginning of the symbol.
64
Measurement Expressions
Definition of symbolTimingAdjust.
The sync argument accepts the following strings: "Short Training Seq", "Channel
Estimation Seq". This argument determines which preamble sequence will be used for
synchronization.
The output argument accepts the following strings (see Available Measurement Results for
evm_wlan_ofdm()): "EVMrms_percent", "EVM_dB", "PilotEVM_dB", "CPErms_percent",
"IQ_Offset_dB", "SyncCorrelation". This argument selects which EVM analysis result will
be returned.
Relationship Between WLAN_802_11a Source Parameters and evm_wlan_ofdm()
Expression Arguments summarizes how some of the arguments of the evm_wlan_ofdm()
expression should be set based on the parameter values of the WLAN_802_11a source.
Relationship Between WLAN_802_11a Source Parameters and evm_wlan_ofdm() Expression Arguments
WLAN_802_11a
evm_wlan_ofdm()
DataRate (default is searchTime (default is
54 Mbps)
80 µsec)
Bandwidth (default
is 20 MHz)
Comments
The recommended searchTime is:
2 BurstLength.
BurstLength= {[5 + (1 + OFDMSymbolsPerBurst)*(1 +
GuardInterval)]*64} / Bandwidth + IdleInterval,
DataLength (default
is 100)
where:
IdleInterval (default
is 4 µsec) †
OFDMSymbolsPerBurst = ceil[(22 + 8 *DataLength)* 250000
/ DataRate]
GuardInterval
(default is 0.25)
MirrorSpectrum
(default is NO)
mirrorSpectrum (default If DUT introduces spectrum mirroring, then mirrorSpectrum
is NO)
must be set to "NO" ("YES") when MirrorSpectrum is set to
"YES" ("NO"); otherwise mirrorSpectrum must be set to the
same value as MirrorSpectrum.
Bandwidth (default
is 20 MHz)
subcarrierSpacing
(default is 312.5 kHz)
GuardInterval
(default is 0.25)
guardInterval (default is guardInterval must be set to the same value as
0.25)
GuardInterval.
subcarrierSpacing must be set to Bandwidth/64.
† The source IdleInterval must be >= 2 sec because the EVM measurement provided by the evm_wlan_ofdm()
needs enough Idle Interval to detect the burst start time.
fs()
Performs a time-to-frequency transform
Syntax
y = fs(x, fstart, fstop, numfreqs, dim, windowType, windowConst, tstart, tstop,
interpOrder, transformMethod)
Arguments
65
Measurement Expressions
Name
Description
Default
Range
Type
Required
x
Time-domain data to be
transformed
None
(-∞:∞)
Real
Yes
fstart
starting frequency
0†
[0:∞)
Real
No
fstop
stoping frequency
1/(2*newdeltat) †
[0:∞)
Real
No
numfreqs
number of frequencies
(fstop-fstart)*(tstoptstart)+1
[1:∞)
Integer
No
dim
dimension to be transformed
(not used currently)
highest dimension
[1:∞)
Integer
No
windowType
type of window to be applied to
the data
0
[0:9] ††
Integer,
string
No
windowConst
window constant †† †
0
[0:∞)
Integer,
Real
No
tstart
start time †† ††
first time point in given [0:∞)
data
Integer,
Real
No
tstop
stop time †† ††
last time point in given [0:∞)
data
Integer,
Real
No
interpOrder
Interpolation Order
1
[1:3] ††
†† †
Integer
No
1
[1:3] ††
†† ††
Integer
No
transformMethod Transformation method
† If data is real, fstart = 0, fstop=1/(2*newdeltat). If data is complex, fstart = 1/(time[startIndex+2]-time[stopIndex]) and fstop=1/(time[startIndex+2]time[stopIndex]). Where newdeltat is the new uniform timestep of the resampled data,
and startIndex and stopIndex are the index of tstart and tstop.
†† The window types and their default constants are:
0 = None
1 = Hamming 0.54
2 = Hanning 0.50
3 = Gaussian 0.75
4 = Kaiser 7.865
5 = 8510 6.0 (This is equivalent to the time-to-frequency transformation with normal gate
shape setting in the 8510 series network analyzer.)
6 = Blackman
7 = Blackman-Harris
8 = 8510-Minimum 0
9 = 8510-Maximum 13
†† † windowConst is not used if windowType is 8510
†† †† If tstart or tstop lies between two time points in the data, then the values are
interpolated for these values.
†† †† † If the tranorder variable is not present, or if the user wishes to override the
interpolation scheme, then interpOrder may be set to a nonzero value:
1 = use only linear interpolation
2 = use quadratic interpolation
3 = use cubic polynomial interpolation
†† †† †† The time-to-frequency transform can be changed by using transformMethod:
66
Measurement Expressions
1 = Chirp-z transform
2 = Discrete Fourier integral evaluated at each frequency
3 = Fast Fourier transform
Examples
The following example equations assume that a transient simulation was
performed from 0 to 5 ns with 176 timesteps, on a 1-GHz-plus-harmonics signal
called vOut:
y=fs(vOut) returns the spectrum (0, 0.2GHz, ... , 17.6GHz), evaluated from 0 to
5 ns.
y=fs(vOut, 0, 10GHz) returns the spectrum (0, 0.2GHz, ... , 10.0GHz), evaluated
from 0 to 5 ns.
y=fs(vOut, 0, 10GHz, 11) returns the spectrum (0, 1.0GHz, ... , 10.0GHz),
evaluated from 0 to 5 ns.
y=fs(vOut, , , , , , , 3ns, 5ns) returns the spectrum (0, 0.5GHz, ... ,
32.0GHz), evaluated from 3 to 5 ns.
y=fs(vOut, 0, 10GHz, 21, , , , 3ns, 5ns) returns the spectrum (0, 0.5GHz, ... ,
10.0GHz), evaluated from 3 to 5 ns.
y=fs(vOut, 0, 10GHz, 11, , "Blackman") returns the spectrum (0, 1.0GHz, ... ,
10.0GHz), evaluated from 0 to 5 ns after a Blackman window is applied.
Defined in
Built in
See Also
fft() (expmeas), fspot() (expmeas)
Notes/Equations
The dim argument is not used and should be left empty in the expression. Entering a
value will have no impact on the results.
fs(x) returns the frequency spectrum of the vector x by using a chirp-z transform. The
values returned are peak, complex values. The data to be transformed is typically from a
transient, signal processing, or envelope analysis.
Transient simulation uses a variable timestep and variable order algorithm. The user sets
an upper limit on the allowed timestep, but the simulator will control the timestep so that
the local truncation error of the integration is also controlled. The non-uniformly sampled
data are uniformly resampled for fs.
If the Gear integration algorithm is used, the order can also change during simulation. fs
can use this information when resampling the data. This variable order integration
depends on the presence of a special dependent variable, tranorder, which is output by
the transient simulator. When the order varies, the Fourier integration will adjust the
order of the polynomial it uses to interpolate the data between timepoints.
67
Measurement Expressions
Only polynomials of degree one to three are supported. The polynomial is fit from the
timepoint in question backwards over the last n points. This is because time-domain data
are obtained by integrating forward from zero; previous data are used to determine future
data, but future data can never be used to modify past data.
The data are uniformly resampled, with the number of points being determined by
increasing the original number of points to the next highest power of two.
The data to be transformed default to all of the data. The user may specify tstart and
tstop
to transform a subset of the data.
The starting frequency defaults to 0 and the stopping frequency defaults to
1/(2*newdeltat), where newdeltat is the new uniform timestep of the resampled data. The
number of frequencies defaults to (fstop-fstart)*(tstop-tstart)+1. The user may change
these by using fstart, fstop, and numfreqs. Note that numfreqs specifies the number of
frequencies, not the number of increments. Thus, to get frequencies at (0, 1, 2, 3, 4, 5),
numfreqs should be set to 6, not 5.
When the data to be operated on is of the baseband type, such as VO[0] from a Circuit
Envelope analysis, where VO is an output node voltage and [0] is index for DC, then in
order to obtain a single sided spectrum, only the real part of VO[0] should be used as the
argument. i.e., x=fs(real(VO[0],...). This is necessary because the fs() function has no
way of knowing the data VO[0] is baseband. Even though VO[0] contains an imaginary
part of all zeroes, it is still represented by a complex data type. When the first argument
of fs() is complex, the result will be a double-sided spectrum by default.
An alternative method of obtaining a single-sided spectrum from the above baseband data
is to specify the frequencies ranges in the spectrum, using the fstart, fstop, and numfreqs
parameters of the fs() function.
For example, y=fs(VO[0], 0, 25e3, 251). This will yield a spectrum from 0 to 25 kHz with
26 frequencies and 1 kHz spacing.
This does not apply to data from Transient analysis or Ptolemy simulation because voltage
data from Transient and baseband data from Ptolemy are real.
For Envelope analysis, the transform is centered around the fundamental tone. For Signal
Processing analysis, it is centered around the characterization frequency.
Differences Between the fs() and fft() Functions
For a periodic signal from t=0 to t=per, fs() requires the full data [0,per], where [] means
0 <= t <= per. The fft is defined as needing data [0,per), meaning 0 <= t < per. The last
point at per should be the same as value at zero. fs() requires this point, fft() does not.
That is why fs() really requires 2n+1 points and fft() requires 2n . So for using the FFT
option in the fs() function, there should be 2n+1 points. However, for the default Chirp Ztransform option, any number of points will work.
Conditions under which fs() may not work properly:
68
Measurement Expressions
1. When deltaF equals 0. Where deltaF = (Fstop - Fstart)/(numFreqs).
2. When 1.0/deltaF > Tstop - Tstart. In this case there are not enough time data for
requested frequency resolution.
3. When 2*numFreqs > numDataPts. In this case there are not enough data points for
frequencies.
Mod_Data_from_1tone_swpUNI()
Returns an amplifier's adjacent and alternate channel power ratios, main channel power,
and error vector magnitude
Syntax
Mod_Data_from_1tone_swpUNI(algorithm, allowextrap, charVoltage, inputSig, sourceZ,
loadZ, mainCh, mainChForPout, lowerAdjCh, upperAdjCh, lowerAltCh, upperAltCh,
winType, winConst)
Arguments
69
Measurement Expressions
Name
Description
algorithm
Default
Range
Type
Required
Specifies the algorithm to be used to model the None
vout-versus-vin data from the HB sweep. Use
"CF" for Curve Fit or "LI" for Linear
Interpolation.
"LI" or
"CF"
String
Yes
allowextrap
Allow or disallow extrapolation when applying
the scaled, modulated input signal to the voutversus-vin model.
1
0, "No",
"NO",
"no", 1,
"Yes",
"YES",
"yes"
String or
Integer
No
charVoltage
This is the characterization voltage (the
fundamental output voltage from the harmonic
balance sweep.) Example: Vload_fund, where
Vload_fund=Vload[1].
None
(-∞:∞)
Complex
Yes
inputSig
This is the input modulated signal (the
envelope.) This signal should be a function of
time, only.
None
(-∞:∞)
Complex
Yes
sourceZ
This is the source impedance. This can be a
swept parameter.
None
(0:∞)
Complex
Yes
loadZ
This is the load impedance. This can be a swept None
parameter.
(0:∞)
Complex
Yes
mainCh
These are the main channel frequency limits, as None
an offset from the carrier frequency. Example:
{(-3.84 MHz/2),(3.84 MHz/2)}
(-∞:∞)
1X2
matrix,
Real or
Integer
Yes
mainChForPout These are the frequency limits used for
None
computing the modulated output power.
Normally these would be the same as the
mainCh argument, but this allows you to specify
a different bandwidth for computing the
modulated output power.
(-∞:∞)
1X2
matrix,
Real or
Integer
Yes
lowerAdjCh
These are the lower adjacent channel frequency None
limits as an offset from the carrier frequency.
Example: MainLimits - (5 MHz)
(-∞:∞)
1X2
matrix,
Real or
Integer
Yes
upperAdjCh
These are the upper adjacent channel frequency None
limits as an offset from the carrier frequency.
Example: MainLimits + (5 MHz)
(-∞:∞)
1X2
matrix,
Real or
Integer
Yes
lowerAltCh
These are the lower alternate channel frequency None
limits as an offset from the carrier frequency.
Example: MainLimits - (10 MHz)
(-∞:∞)
1X2
matrix,
Real or
Integer
Yes
upperAltCh
These are the upper alternate channel
frequency limits as an offset from the carrier
frequency. Example: MainLimits + (10 MHz)
None
(-∞:∞)
1X2
matrix,
Real or
Integer
Yes
winType
window type
"Kaiser"
†
string
No
winConst
window constant that affects the shape of the
applied window.
depends
on
winType
used
[0:∞)
Real
No
† winType can be: "none", "hamming", "hanning", "gaussian", "kaiser", "8510",
"blackman","blackman-harris"
Examples
70
Measurement Expressions
Vload_fundHB=Vload[1]
Vin_fund=_3GPPFDD_UE_Tx_12_2_SigGen..Vsource
Zsource=50
Zload=50
MainLimits={-3.84 MHz/2,3.84 MHz/2}
MainLimitsForPout=MainLimits
LoChLimits=MainLimits-(5 MHz)
UpChLimits=MainLimits+(5 MHz)
LoChLimitsAlt=MainLimits-(10 MHz)
UpChLimitsAlt=MainLimits+(10 MHz)
Data_DDS=Mod_Data_from_1tone_swpUNI("LI", "Yes", Vload_fundHB, Vin_fund,
Zsource, Zload, MainLimits, MainLimitsForPout, LoChLimits, UpChLimits,
LoChLimitsAlt, UpChLimitsAlt, "Kaiser",)
ACPR_dBc=Data_DDS(0)
Pout_dBm=Data_DDS(2)
ACPR_vs_Pout=vs(ACPR_dBc,Pout_dBm)
AltCPR_dBc=Data_DDS(1)
AltCPR_vs_Pout=vs(AltCPR_dBc,Pout_dBm)
EVM_percent=Data_DDS(3)
EVM_vs_Pout=vs(EVM_percent,Pout_dBm)
See Also
ACPR_ChPwr_or_EVM_from_1toneSwp() (expmeas)
Notes/Equations
This function returns the adjacent and alternate channel power ratios, main channel
power, and EVM. Because it returns multiple results, it cannot be used in a measurement
expression on the schematic. It can only be used in the data display.
The advantage of using this function instead of ACPR_ChPwr_or_EVM_from_1tone_swp()
is that it is more efficient for obtaining all these results. When using
ACPR_ChPwr_or_EVM_from_1tone_swp(), you have to call it once to get the adjacent
channel power ratios, once again to get the alternate channel power ratios, once again to
get the main channel power, and once again to get the EVM. The big disadvantage of
using the Mod_Data_from_1tone_swpUNI() is that this function will get executed each
time you open a data display that contains it. While it is slower to use the
ACPR_ChPwr_or_EVM_from_1tone_swp() function on the schematic, the advantage is that
the results are written into the dataset, and data displays that show these results open
instantly.
For EVM, the single-tone method is not specification-compliant. It just measures the “raw”
EVM, computed at each time point. The EVM is computed after correcting for the average
phase difference and RMS amplitude difference between the output and input modulated
signals. If the modulated signal at the output of the amplifier has only a constant phase
shift and a constant gain (meaning that neither vary with the amplitude of the input
modulated signal), then the EVM will be zero. With this method, the EVM is computed at
each time point, not at just the symbol times. There is no demodulation or decoding of the
signal, so you can’t calculate the EVM of each sub-carrier, say for an LTE signal.
For ACPR, the single-tone method does not include any receive-side filtering. It just
generates the spectrum at the output of the amplifier, integrates the power in the main,
adjacent, and alternate channels, then computes the ratios. The single-tone method of
71
Measurement Expressions
computing EVM (and ACPR) will tend to become less accurate as the bandwidth of the
signal gets larger. This is because this method assumes the response of the amplifier is
constant across the modulation bandwidth (we’re modeling the nonlinearity by injecting a
single tone at the carrier frequency, after all.)
peak_pwr()
Returns the peak power of the input voltage data
Syntax
peakP = peak_pwr(voltage, refR, percent, unit)
Arguments
Name Description
Default Range
Type
Required
voltage baseband or complex envelope voltage
signal
None
(-∞:∞)
Integer, Real,
Complex
Yes
refR
50.0
(0:∞)
Real
No
percent percentage of time the returned power
value is exceeded
reference resistance in Ohms
0.0
[0:100]
Real
No
unit
"W"
"W","dBm","dBW" string
power unit to be used
No
Examples
peakP = peak_pwr(Vout[1], 100, , "dBW")
where Vout is a named node in a Circuit Envelope simulation, will return the
peak power (in dBW) at the fundamental frequency using 100 Ohms as reference
resistance.
peakP = peak_pwr(T1, , 5)
where T1 is the name of a TimedSink component (in a DSP schematic), will return
the power level (in W) that is exceeded 5% of the time for the voltage signal
recorded in the TimedSink using 50 Ohms as reference resistance. If the signal
recorded by the TimedSink is complex envelope Gaussian noise with a standard
deviation of 30 mV for each of the I and Q envelopes, then peakP will be very
close to 5.39e-5 W ( -ln(0.05) / 0.032 / 50 ).
Defined in
$HPEESOF_DIR/expressions/ael/digital_wireless_fun.ael
See Also
peak_to_avg_pwr() (expmeas), power_ccdf() (expmeas), pwr_vs_t() (expmeas),
total_pwr() (expmeas)
Notes/Equations
Used in Circuit Envelope and Signal Processing simulations.
This expression can be used with input data (voltage) of any dimensions when the percent
argument is 0 and up to three dimensions when the percent argument is greater than 0. It
72
Measurement Expressions
can handle both baseband as well as complex envelope data.
When the percent argument is set to 0, the returned value is the maximum instantaneous
power of the input voltage signal. When the percent argument is set to a value greater
than 0, the returned value is the power level that is exceeded for percent amount of time.
This argument is useful since some wireless standards specify the peak power not as the
absolute maximum instantaneous power but as the power level that is exceeded for some
percentage of time. For example, the 3GPP standard defines the maximum power as the
power level that is exceeded for 1% of the time.
peak_to_avg_pwr()
Returns the peak to average power ratio of the input voltage data
Syntax
peak_avg_ratio = peak_to_avg_pwr(voltage, percent, unit)
Arguments
Name Description
Default Range
Type
Required
voltage baseband or complex envelope voltage signal
None
(-∞:∞)
Integer, Real,
Complex
Yes
percent percentage of time the returned power value is
exceeded
0.0
[0:100]
Real
No
unit
"dB"
"dB","ratio" string
unit to be used
No
Examples
peak_avg_ratio = peak_to_avg_pwr(Vout[1], , "ratio")
where Vout is a named node in a Circuit Envelope simulation, will return the
peak to average power ratio (as a ratio) at the fundamental frequency.
peak_avg_ratio = peak_to_avg_pwr(T1, 5, "ratio")
where T1 is the name of a TimedSink component (in a DSP schematic), will return
the ratio of the power level that is exceeded 5% of the time to the average
power level for the voltage signal recorded in the TimedSink. If the signal
recorded by the TimedSink is complex envelope Gaussian noise with the same
standard deviation for both the I and Q envelopes, then peak_avg_ratio will be
very close to 2.99 ( -ln(0.05) ).
peak_avg_ratio = peak_to_avg_pwr(T1)
where T1 is the name of a TimedSink component (in a DSP schematic), will return
the peak to average power ratio (in dB) for the voltage signal recorded in the
TimedSink. If the signal recorded by the TimedSink is an ideal QPSK signal
(filtered using a raised cosine filter of ExcessBW 0.5), then peak_avg_ratio
will be very close to 3.95 dB. If the signal recorded by the TimedSink is an
ideal /4-DQPSK signal (filtered using a raised cosine filter of ExcessBW 0.5),
then peak_avg_ratio will be very close to 3.3 dB.
Defined in
$HPEESOF_DIR/expressions/ael/digital_wireless_fun.ael
73
Measurement Expressions
See Also
peak_pwr() (expmeas), power_ccdf() (expmeas), pwr_vs_t() (expmeas), total_pwr()
(expmeas)
Notes/Equations
Used in Circuit Envelope and Signal Processing simulations.
This expression can be used with input data (voltage) of any dimensions when the percent
argument is 0 and up to three dimensions when the percent argument is greater than 0.
The expression can accommodate both baseband as well as complex envelope data.
The peak to average ratio is computed by calling the peak_pwr() and total_pwr()
expressions and then taking the ratio of the two values returned by these expressions.
The percent argument is used for the calculation of the peak power value. For the use and
meaning of the percent argument see the peak_pwr() (expmeas) Notes/Equations.
Since a ratio of power values is calculated a reference resistance is not needed for this
measurement.
power_ccdf()
Returns the power CCDF (Complementary Cumulative Distribution Function) curve for the
input voltage/current data.
Syntax
pCCDF = power_ccdf(data, numBins)
Arguments
Name
Description
Default
Range Type
Required
data
baseband or complex envelope
voltage/current signal
None
(∞:∞)
Integer, Real,
Complex
Yes
Integer
No
numBins number of points in the returned power
CCDF curve
log2(numDataPoints) [1:∞)
Examples
pCCDF = power_ccdf(Vout[1])
where Vout is a named node in a Circuit Envelope simulation, will return the
power CCDF curve for the voltage at the fundamental frequency. The returned
power CCDF curve will have the default number of points.
pCCDF = power_ccdf(T1, 10)
where T1 is the name of a TimedSink component (in a DSP schematic), will return
the power CCDF curve for the voltage signal recorded in the TimedSink. The
returned curve will have 10 points.
Defined in
$HPEESOF_DIR/expressions/ael/digital_wireless_fun.ael
74
Measurement Expressions
See Also
peak_pwr() (expmeas), peak_to_avg_pwr() (expmeas), power_ccdf_ref() (expmeas),
pwr_vs_t() (expmeas), total_pwr() (expmeas)
Notes/Equations
Used in Circuit Envelope and Signal Processing simulations.
This expression can be used with input data of up to two dimensions. It can accommodate
both baseband as well as complex envelope data.
The power CCDF (typically called just CCDF) measurement is a very common
measurement performed on 2G and 3G wireless signals. The CCDF curve shows the
probability that the instantaneous signal power will be higher than the average signal
power by a certain amount of dB. The independent axis of the CCDF curve shows power
levels in dB with respect to the signal average power level (0 dB corresponds to the signal
average power level). The dependent axis of the CCDF curve shows the probability that
the instantaneous signal power will exceed the corresponding power level on the
independent axis. CCDF Curve for WLAN 802.11a 54 Mbps Signal shows the CCDF curve
for a WLAN 802.11a 54 Mbps signal.
CCDF Curve for WLAN 802.11a 54 Mbps Signal
75
Measurement Expressions
In CCDF Curve for WLAN 802.11a 54 Mbps Signal, you can see that the instantaneous
signal power exceeds the average signal power (0 dB) for 20% of the time. You can also
see that the instantaneous signal power exceeds the average signal power by 5 dB for
only 0.3% of the time.
power_ccdf_ref()
Returns the power CCDF (Complementary Cumulative Distribution Function) curve for
white gaussian noise.
Syntax
ccdfRef = power_ccdf_ref(indepPowerRatioValues)
Arguments
Name
Description
Default Range Type
indepPowerRatioValues power levels (in dB with respect to the average None
power level of a white gaussian noise signal) at
which the power CCDF for white gaussian noise
will be calculated
(∞:∞)
Integer,
Real
Required
Yes
Examples
pCCDF = power_ccdf(T1)
ccdfRef = power_ccdf_ref( indep( pCCDF) )
where T1 is the name of a TimedSink component (in a DSP schematic),
the power CCDF curve for white gaussian noise evaluated at the same
levels as the pCCDF curve.
ccdfRef = power_ccdf_ref( [-10::2::8] )
will return the power CCDF curve for white gaussian noise evaluated
power levels -10, -8, -6, -4, -2, 0, 2, 4, 6, 8 (in dB with respect
average power level of a white gaussian noise signal).
will return
power
at the
to the
Defined in
$HPEESOF_DIR/expressions/ael/digital_wireless_fun.ael
See Also
power_ccdf() (expmeas)
Notes/Equations
This expression can be used with input data of up to two dimensions.
The input data must be sorted in increasing or decreasing order. In addition, it is
recommended that the input vector argument has uniformly spaced values. The vector
"indep( X )", where X is the value returned by the power_ccdf() expression, is guaranteed
to have uniformly spaced values sorted in increasing order. This would be the most typical
value for the input argument of power_ccdf_ref().
76
Measurement Expressions
A typical power CCDF measurement (see Notes/Equations for power_ccdf() (expmeas))
provides a reference CCDF curve along with the measured CCDF curve. This reference
curve is typically the power CCDF curve for a white gaussian noise signal. This expression
can generate this reference curve. CCDF Curve for WLAN 802.11a Signal with Reference
Curve shows the CCDF curve for a WLAN 802.11a signal along with the reference curve.
CCDF Curve for WLAN 802.11a Signal with Reference Curve
pwr_vs_t()
Returns the power vs. time waveform for the input voltage data
Syntax
p_vs_t = pwr_vs_t(voltage, refR, unit)
Arguments
Name Description
Default Range
Type
Required
voltage baseband or complex envelope voltage
signal
None
(-∞:∞)
Integer, Real,
Complex
Yes
refR
reference resistance in Ohms
50.0
(0:∞)
Real
No
unit
power unit to be used
"W"
"W","dBm","dBW" string
Examples
p_vs_t = pwr_vs_t(Vout[1], 100, "dBm")
77
No
Measurement Expressions
where Vout is a named node in a Circuit Envelope simulation, will return the
power (in dBm) vs. time waveform for the voltage at the fundamental frequency
using 100 Ohms as reference resistance.
p_vs_t = pwr_vs_t(T1)
where T1 is the name of a TimedSink component (in a DSP schematic), will return
the power (in W) vs. time waveform for the voltage signal recorded in the
TimedSink using 50 Ohms as reference resistance.
Defined in
$HPEESOF_DIR/expressions/ael/digital_wireless_fun.ael
See Also
peak_pwr() (expmeas), peak_to_avg_pwr() (expmeas), power_ccdf() (expmeas),
total_pwr() (expmeas)
Notes/Equations
Used in Circuit Envelope and Signal Processing simulations.
This expression can be used with input data (voltage) of any dimensions. It can
accommodate both baseband as well as complex envelope data.
relative_noise_bw()
Computes the relative noise bandwidth of the smoothing windows used by the fs()
function
Syntax
y = relative_noise_bw(winType, winConst)
Arguments
Name
Description
Default Range Type Required
winType window type
None
winConst window constant that affects the shape of the applied window. 0.75
†
string No
[0:∞)
Real
No
† winType can be: "none", "hamming", "hanning", "gaussian", "kaiser", "8510",
"blackman","blackman-harris"
Examples
winType = "Kaiser"
winConst = 8
relNoiseBW = relative_noise_bw("Kaiser", 8) = 1.666
Vfund=vOut[1]
VoltageSpectralDensity = fs(Vfund, , , , , winType, winConst)
PowerSpectralDensity = 0.5 * mag(VoltageSpectralDensity**2)/50/relNoiseBW
where vOut is the named connection at a 50-ohm load, and it is an output from a
Circuit Envelope simulation.
78
Measurement Expressions
Note vOut is a named connection on the schematic. Assuming that a Circuit
Envelope simulation was run, vOut is output to the dataset as a two-dimensional
matrix. The first dimension is time, and there is a value for each time point
in the simulation. The second dimension is frequency, and there is a value for
each fundamental frequency, each harmonic, and each mixing term in the
analysis, as well as the baseband term.
vOut[1] is the equivalent of vOut[::, 1], and specifies all time points at the
lowest non-baseband frequency (the fundamental analysis frequency, unless a
multitone analysis has been run and there are mixing products). For former MDS
users, the notation "vOut[*, 2]" in MDS corresponds to the notation of
"vOut[1]".
Defined in
$HPEESOF_DIR/expressions/ael/digital_wireless_fun.ael
See Also
acpr_vi() (expmeas), acpr_vr() (expmeas), channel_power_vi() (expmeas),
channel_power_vr() (expmeas), fs() (expmeas)
Notes/Equations
Used in The following functions: acpr_vi, acpr_vr, channel_power_vi, channel_power_vr.
The relative noise bandwidth function is used to account for the fact that as windows are
applied, the effective noise bandwidth increases with respect to the normal resolution
bandwidth. The resolution bandwidth is determined by the time span and not by the
displayed frequency resolution.
sample_delay_pi4dqpsk()
This function calculates the optimal sampling point within a symbol for a given pi4dqpsk
waveform. "Optimal" is defined as the sampling point that provides the lowest bit error
rate.
Syntax
y = sample_delay_pi4dqpsk(vlQ, symbolRate, path_delay, timeResolution)
Arguments
79
Measurement Expressions
Name
Description
Default Range Type
vlQ
complex envelope (I + j * Q) of a pi/4 DQPSK signal
None
(∞:∞)
Complex Yes
symbolRate
symbol rate of the pi/4 DQPSK signal
None
(0:∞)
Real
Yes
path_delay
time delay on the waveform before the sampling starts † None
(0:∞)
Real
Yes
(0:∞)
Real
Yes
timeResolution time step (typically one-tenth of a symbol time or less)
used to search for the best sampling point in a given
symbol period
None
Required
† If the delay is 0, this parameter may be omitted. If it is non-zero, enter the delay value.
This can be calculated using the function delay_path().
Examples
a = sample_delay_pi4dqpsk(vout[1], 25e3, 1.5e-6, 0.15e-6)
Defined in
Built in
See Also
ber_pi4dqpsk() (expmeas), ber_qpsk() (expmeas), const_evm() (expmeas)
Notes/Equations
This function can be used only with 1-dimensional data.
sample_delay_qpsk()
This function calculates the optimal sampling point within a symbol for a given QPSK
waveform."Optimal" is defined as the sampling point that provides the lowest bit error
rate.
Syntax
y = sample_delay_qpsk(vlQ, symbolRate, path_delay, timeResolution)
Arguments
Name
Description
Default Range Type
vlQ
complex envelope (I + j * Q) of a QPSK signal
None
(∞:∞)
Complex Yes
symbolRate
symbol rate of the QPSK signal
None
(0:∞)
Real
Yes
path_delay
time delay on the waveform before the sampling starts † None
(0:∞)
Real
Yes
(0:∞)
Real
Yes
timeResolution time step (typically one-tenth of a symbol time or less)
used to search for the best sampling point in a given
symbol period
None
Required
† If the delay is 0, this parameter may be omitted. If it is non-zero, enter the delay value.
This can be calculated using the function delay_path().
80
Measurement Expressions
Examples
a = sample_delay_qpsk(vout[1], 25e3, 1.5e-6, 0.15e-6)
Defined in
Built in
See Also
ber_pi4dqpsk() (expmeas), ber_qpsk() (expmeas), const_evm() (expmeas)
Notes/Equations
This function can be used only with 1-dimensional data.
Note
This function is only available in 32-bit simulator.
spectrum_analyzer()
Performs a spectrum analysis for the input voltage/current data
Syntax
spectrum = spectrum_analyzer(data, fCarrier, start, stop, window, resBW)
Arguments
Name Description
data
Default
baseband or complex envelope voltage/current None
signal
Range Type
Required
(∞:∞)
Real,
Complex
Yes
No
fCarrier frequency around which the spectrum will be
centered
0
[0:∞)
Real
start
start time for the spectrum analysis
first point of input
data
[0:∞)
Integer, Real No
stop
stop time for the spectrum analysis
last point of input
data
[0:∞)
Integer, Real No
window type of window to be used
0
[0:7] † Integer,
string
resBW
0
[0:∞)
resolution bandwidth
No
Integer, Real No
† See Notes for the window type.
Examples
spectrum = spectrum_analyzer(Vout[1])
where Vout is a named node in a Circuit Envelope simulation, will return the
voltage spectrum at the fundamental frequency. The spectrum will be centered
81
Measurement Expressions
around 0 Hz. All the input data will be processed in one block resulting in the
highest resolution bandwidth possible. No windowing will be done.
spectrum = spectrum_analyzer(Vout[1], 3.5e9, , , "Kaiser 7.865", 30e3)
where Vout is a named node in a Circuit Envelope simulation, will return the
voltage spectrum at the fundamental frequency. The spectrum will be centered
around 3.5 GHz. The input signal will be broken down in smaller segments in
order to achieve 30 kHz of resolution bandwidth. All segments will be windowed
with a Kaiser 7.865 window. The spectra of all segments will be averaged.
spectrum = spectrum_analyzer(T1, , 1.0e-3, 2.0e-3, "Hanning 0.5")
where T1 is the name of a TimedSink component (in a DSP schematic), will return
the voltage spectrum for the segment between 1 msec and 2 msec of the signal
recorded in the TimedSink. Of course, the TimedSink component must have
recorded a signal that starts before 1 msec and ends after 2 msec. The spectrum
will be centered around 0 Hz. A Hanning 0.5 window will be used.
Defined in
Built in
See Also
fs() (expmeas)
Notes/Equations
Used in Circuit Envelope and Signal Processing simulations.
This expression can be used with input data of up to two dimensions. It can handle both
baseband as well as complex envelope input data. Although non-uniformly sampled data is
supported, it is recommended to use this expression with uniformly sampled data.
The spectrum_analyzer() expression returns the voltage or current spectrum of the input
(voltage or current) signal. The returned values are the complex amplitude voltages or
currents at the frequencies of the spectral tones. The returned values are not the powers
at the frequencies of the spectral tones. However, one can calculate and display the power
spectrum by using the dbm() (expmeas) expression (for voltage input data) or writing a
simple equation (for current input data) in the data display window.
Note that, for baseband signals and for the frequency of 0 Hz, the dBm function returns a
power value that is 3 dB less than the actual power. This is because the primary use of
the dBm function is with RF signals, where the 0 Hz frequency corresponds to the carrier
frequency and not really 0 Hz signal frequency. If the baseband signal has no significant
power at DC, this 3 dB error is insignificant and can be ignored-otherwise, it must be
considered.
The basis of the algorithm used by the spectrum_analyzer() expression is the fs()
(expmeas) expression (the chirp-Z transform option of fs() is used). The input data can be
processed as one block and the spectrum calculated over the entire input signal.
Alternatively, the input signal can be broken down in smaller blocks and the spectra of all
82
blocks averaged.
Measurement Expressions
The fCarrier argument sets the frequency around which the spectrum will be centered.
This is only true for a complex envelope signal. For baseband signals, this argument is
ignored. The spectrum span is:
for complex envelope signals [fCarrier-0.5/TStep, fCarrier+0.5/TStep]
for baseband signals [0, 0.5/TStep]
where TStep is the simulation time step.
If it is not desirable to process all the input data, the start and stop arguments can be
used to define a segment of the input data to be processed. This can be useful when
trying to exclude parts of the signal where transients occur.
The window argument sets the window that will be used to window the input data.
Windowing is often necessary in transform-based (chirp-Z, FFT) spectrum estimation.
Without windowing, the estimated spectrum may suffer from spectral leakage that can
cause misleading measurements or masking of weak signal spectral detail by spurious
artifacts. If the input data is broken down in multiple blocks then the window is applied to
each block.
The window argument accepts the following strings: "none", "Hamming 0.54", "Hanning
0.50", "Gaussian 0.75", "Kaiser 7.865", "8510 6.0", "Blackman", "Blackman-Harris". The
equations defining these windows are given below:
none:
where N is the window size
Hamming 0.54:
where N is the window size
Hanning 0.5:
where N is the window size
Gaussian 0.75:
where N is the window size
Kaiser 7.865:
83
Measurement Expressions
where N is the window size, α = N / 2, and I0(.) is the 0th order modified Bessel
function of the first kind
8510 6.0 (Kaiser 6.0):
where N is the window size, α = N / 2, and I0(.) is the 0th order modified Bessel
function of the first kind
Blackman:
where N is the window size
Blackman-Harris:
where N is the window size
The resBW parameter can be used to set the spectrum measurement resolution
bandwidth. If set to 0, it is ignored and the signal segment defined by start and stop is
processed as one segment. In this mode of operation, the returned spectrum will have the
highest possible resolution bandwidth (resolution bandwidth is inversely proportional to
the input signal length). If resBW is set to a value greater than 0, then the input signal
segment defined by start and stop is broken down in smaller subsegments of the
appropriate length. The length of each segment is decided based on the value of resBW
and the selected window. The spectrum of each subsegment is calculated and averaged
with the spectra of the other subsegments. In this mode of operation, the resolution
bandwidth achieved is resBW. Averaging multiple input signal segments. shows an
example where the input signal is broken down in multiple segments. As can be seen in
this figure, if an exact integer multiple of subsegments cannot fit in the segment defined
by start and stop, then part of the signal may not be used.
84
Measurement Expressions
Averaging multiple input signal segments.
In an analog swept spectrum analyzer, the resolution bandwidth is determined by the last
in a series of analog IF filters. In contrast, the spectrum_analyzer() expression calculates
the spectrum using DSP algorithms and so the resolution bandwidth is determined by the
length of the input data segment the algorithm processes and the selected window.
ResBW = ENBW = NENBW / T
where ENBW is the window equivalent noise bandwidth
T is the length of the input data segment in seconds and
NENBW is the window normalized equivalent noise bandwidth The following table shows
the NENBW values for the available windows).
Window
NENBW
none
1.0
Hamming 0.54
1.363
Hanning 0.5
1.5
Gaussian 0.75
1.883
Kaiser 7.865
1.653
8510 6.0
1.467
Blackman
1.727
Blackman-Harris 2.021
The equivalent noise bandwidth (ENBW) of a window is defined as the width of a
rectangular filter that passes the same amount of white noise as the window. The
normalized equivalent noise bandwidth (NENBW) is computed by multiplying ENBW with
the time record length. For example, a Hanning window with a 0.5 second input data
segment will result in an ENBW (as well as ResBW) of 3 Hz (1.5 / 0.5).
How to choose the right window
Every time a window is applied to a signal (Window = none effectively applies a
rectangular window to the signal), leakage occurs, that is, power from one spectral
component leaks into the adjacent ones. Leakage from strong spectral components can
result in hiding/masking of nearby weaker spectral components. Even strong spectral
components can be affected by leakage. For example, two strong spectral components
close to each other can appear as one due to leakage.
Choosing the right window for a spectral measurement is very important. The choice of
window depends on what is being measured and what the trade-offs between frequency
resolution (ability to distinguish spectral components of comparable strength that are
close to each other) and dynamic range (ability to measure signals with spectral
components of widely varying strengths and distributed over a wide range) are.
85
Measurement Expressions
As described above, windows can be characterized by their Normalized Equivalent Noise
Bandwidth (NENBW). In general, for the same length of signal processed, the higher the
NENBW of a window the higher its dynamic range (less leakage) and the poorer its
frequency resolution.
Some general guidelines for choosing a window are given below:
Do not use a window (Window = none) when analyzing transients.
For periodic signals whose spectral components have comparable strengths and when
the signal segment processed includes an exact integer multiple of periods, the best
results are obtained if no window is used (Window = none, which is equivalent to
using a rectangular window). Any start up transients should be excluded.
For periodic signals whose spectral components have significantly different strengths
and/or when the signal segment processed does not include an exact integer multiple
of periods, the use of a window can improve the detection of the weaker spectral
components. The higher the NENBW the more likely the weaker spectral components
will be detected. However, this trades-off frequency resolution and so if the spectral
components are very close to each other the weaker one might remain unresolved.
To improve frequency resolution while still maintaining a good dynamic range use a
window but process a longer signal segment.
For aperiodic signals such as modulated signals (QPSK, QAM, GSM, EDGE, CDMA,
OFDM) the use of a window is highly recommended. The window will attenuate the
signal at both ends of the signal segment processed to zero. This makes the signal
apear periodic and reduces leakage.
total_pwr()
Returns the total (average) power of the input voltage data
Syntax
totalP = total_pwr(voltage, refR, unit)
Arguments
Name Description
Default Range
Type
Required
voltage baseband or complex envelope voltage
signal
None
(-∞:∞)
Integer, Real,
Complex
Yes
refR
reference resistance in Ohms
50.0
(0:∞)
Real
No
unit
power unit to be used
"W"
"W","dBm","dBW" string
No
Examples
totalP = total_pwr(Vout[1], 100, "dBm")
where Vout is a named node in a Circuit Envelope simulation, will return the
total power (in dBm) at the fundamental frequency using 100 Ohms as reference
resistance.
totalP = total_pwr(T1)
where T1 is the name of a TimedSink component (in a DSP schematic), will return
the total power (in W) for the voltage signal recorded in the TimedSink using
50 Ohms as reference resistance. If the signal recorded by the TimedSink is
baseband Gaussian noise with a standard deviation of 30 mV, then totalP will be
very close to 1.8e-5 W ( 0.032 / 50 ).
86
Measurement Expressions
Defined in
$HPEESOF_DIR/expressions/ael/digital_wireless_fun.ael
See Also
peak_pwr() (expmeas), peak_to_avg_pwr() (expmeas), power_ccdf() (expmeas),
pwr_vs_t() (expmeas)
Notes/Equations
Used in Circuit Envelope and Signal Processing simulations.
This expression can be used with input data (voltage) of any dimensions. It can
accommodate both baseband as well as complex envelope data.
trajectory()
Generates the trajectory diagram from I and Q data, which are usually produced by a
Circuit Envelope simulation.
Syntax
Traj = trajectory(i_data, q_data)
Arguments
Name Description
Default Range Type
Required
i_data in-phase component of data versus time of a single complex
voltage spectral component (for example, the fundamental) †
None
(∞:∞)
Complex Yes
q_data quadrature-phase component of data versus time of a single
complex voltage spectral component (for example, the
fundamental) †
None
(∞:∞)
Complex Yes
† This could be a baseband signal instead, but in either case it must be real valued versus
time.
Examples
Rotation = -0.21
Vfund=vOut[1] *exp(j * Rotation)
Vimag = imag(Vfund)
Vreal = real(Vfund)
Traj = trajectory(Vreal, Vimag)
where Rotation is a user-selectable parameter that rotates the trajectory
diagram by that many radians and vOut is the named connection at a node.
Note vOut is a named connection on the schematic. Assuming that a Circuit
Envelope
simulation was run, vOut is output to the dataset as a two-dimensional matrix.
The first dimension is time, and there is a value for each time point in the
simulation. The second dimension is frequency, and there is a value for each
fundamental frequency, each harmonic, and each mixing term in the analysis, as
well as the baseband term.
vOut[1] is the equivalent of vOut[::, 1], and specifies all time points at the
87
Measurement Expressions
lowest non-baseband frequency (the fundamental analysis frequency, unless a
multitone analysis has been run and there are mixing products). For former MDS
users, the notation "vOut[*, 2]" in MDS corresponds to the notation of
"vOut[1]".
Defined in
$HPEESOF_DIR/expressions/ael/digital_wireless_fun.ael
See Also
constellation() (expmeas), const_evm() (expmeas)
Notes/Equations
Used in Trajectory diagram generation.
The I and Q data do not need to be baseband waveforms. For example, they could be the
in-phase (real or I) and quadrature-phase (imaginary or Q) part of a modulated carrier.
The user must supply the I and Q waveforms versus time.
88
Measurement Expressions
Data Access Functions for Measurement Expressions
This section describes data access and data manipulation functions in detail. The functions
are listed in alphabetical order.
You can use these functions to find information about a piece of data (e.g., independent
values, size, type, attributes, etc.). You can also use some functions to generate data for
plotting circles and contours.
Note
For information on how these functions are used, see the tutorial example Using Expressions in the Data
Display Window (examples).
build subrange() (expmeas)
chop() (expmeas)
chr() Measurement (expmeas)
circle() (expmeas)
collapse() (expmeas)
contour_ex() (expmeas)
contour() (expmeas)
contour polar() (expmeas)
copy() (expmeas)
create() (expmeas)
dd_threshold() (expmeas)
delete() (expmeas)
expand() (expmeas)
find() (expmeas)
find index() (expmeas)
generate() (expmeas)
get attr() (expmeas)
get indep values() (expmeas)
indep() (expmeas)
max index() (expmeas)
min index() (expmeas)
permute() (expmeas)
plot vs() (expmeas)
set attr() (expmeas)
size() (expmeas)
sort() (expmeas)
sweep dim() (expmeas)
sweep size() (expmeas)
type() (expmeas)
vs() (expmeas)
what() (expmeas)
write var() (expmeas)
build_subrange()
Builds the subrange data according to the innermost independent range. Use with all
swept data
Syntax
y = build_subrange(data, innermostIndepLow, innermostIndepHigh)
89
Measurement Expressions
Arguments
Name
Description
Default
data
analysis results or user None
input.
Range Type
Required
(∞:∞)
Integer, Real, Yes
Complex
innermostIndepLow lowest value of
minimum value of the inner
innermost independent most independent variable
(∞:∞)
Integer, Real, No
Complex
innermostIndepHigh highesr value of
maximum value of the inner
innermost independent most independent variable
(∞:∞)
Integer, Real, No
Complex
Examples
Given S-parameter data swept as a function of frequency with a range of 100 MHz
to 500 MHz, find the values of S12 in the range of 200 MHz to 400 MHz.
subrange_S12 = build_subrange(S12, 200MHz, 400MHz)
Defined in
$HPEESOF_DIR/expressions/ael/statistical_fun.ael
chop()
Replace numbers in x with magnitude less than dx with 0
Syntax
y = chop(x, dx)
Arguments
Name Description
Default Range Type
Required
x
numbers to replace None
(∞:∞)
Integer, real, complex Yes
dx
value to compare to 1e-10
(∞:∞)
Integer, real, complex Yes
Examples
chop(1) returns 1
chop(1e-12) returns 0
chop(1+1e-12i) returns 1+0i
Defined in
$HPEESOF_DIR/expressions/ael/elementary_fun.ael
Notes/Equations
The chop() function acts independently on the real and complex components of x,
comparing each to mag(dx). For example,
y = x if mag(x) >= mag(dx)
y = 0 if mag(x)
90
Measurement Expressions
chr()
Returns the character representation of an integer
Syntax
y = chr(x)
Arguments
Name Description
x
Default Range Type
valid number representing a ASCII character None
Required
[0:127] Integer Yes
Examples
a = chr(64) returns @
a = chr(60) returns <
a = chr(117) returns u
Defined in
Built in
Note
The function name chr() is used for more than one type of expression. For comparison, see the AEL
Function chr() Function (ael). Also, for more information on the different expression types and the
contexts in which they are used, see Duplicated Expression Names (expmeas).
circle()
Used to draw a circle on a Data Display page. Accepts the arguments center, radius, and
number of points. Can only be used on polar plots and Smith charts.
Syntax
a = circle(center, radius, numPts)
Arguments
Name Description
Default Range Type
Required
center center coordinate
None
(∞:∞)
Integer, real,
Complex
Yes
radius
None
[0:∞)
Integer, real
Yes
numPts number of points in the circle None
[0:∞)
Integer
Yes
radius
Examples
x = circle(1,1,500)
y = circle(1+j*1,1,500)
Defined in
Built in
91
Measurement Expressions
collapse()
Collapses the inner independent variable and returns one dimensional data
Syntax
y = collapse(x)
Arguments
Name Description
Default Range Type
Required
x
None
Yes
multi-dimensional data to be collapsed (dimension is
larger than one and less than four)
(∞:∞)
Integer, real,
complex
Examples
Given monte carlo analysis results for the S11 of a transmission line:
It is two-dimensional data: the outer sweep is mcTrial; the inner sweep is the
frequency from 100 MHz to 300 MHz and is given in the following format:
mcTrial freq S11
1 100MHz 0.2
200MHz 0.4
300MHz 0.6
2 100MHz 0.3
200MHz 0.5
300MHz 0.7
Returns a one dimensional data with mcTrail, containing all of the previous
data:
collapsed_S11 = collapse(S11)
mcTrial S11
1 0.2
1 0.4
1 0.6
2 0.3
2 0.5
2 0.7
Defined in
$HPEESOF_DIR/expressions/ael/statistical_fun.ael
See Also
expand() (expmeas)
Notes/Equations
The collapse() function cannot be used to convert a matrix into an array or vector. Use the
expand() function instead.
92
Measurement Expressions
contour_ex()
Generates contours at desired levels that you specify, or at "round number" values on
polar, or rectangular surface data
Syntax
Response1_Contours=contour_ex(data, rect_or_polar, step_size, num_lines,
desired_levels, interp_type, min_or_max, data_format)
Arguments
Name
Description
Default Range
Type
Required
data
2-dimensional, or 3-dimensional
data
None
Real
Yes
(-∞:∞)
rect_or_polar specifies whether to use the
contour() or contour_polar()
function internally
"POLAR" (0, 1), or ("RECT",
integer/string
or 1
"POLAR")
0/"RECT" - use
contour(), 1/"POLAR"
- use contour_polar()
No
step_size
step size between contour lines,
a single real or integer number
1
(0:∞)
Real or Integer
No
num_lines
number of contour lines
requested
5
[1:∞)
Real or Integer
No
None
(-∞:∞)
Real or Integer
single value or
array
No
integer
No
desired_levels specific desired contour levels
interp_type
specifies the type of interpolation 2
to perform
(0, 1, 2) 0 - No
Interpolation, 1 Cubic Spline, 2 - BSpline
min_or_max
boolean variable that specifies
1
whether the contours are to be
drawn from the maximum value
down or from the minimum value
up
(0, 1), or ("Min",
integer or string No
"Max")
0/"Min", from the
minimum value up
1/"Max", from the
maximum value down
data_format
specifies data format. It is
required for the polar contour
plot
"RI"/"MA"
"RI"
string
No
Examples
polar contours
Response1=PAE
StepSize=1
Num_Lines=5
InterpType=2
Response1_Contours=contour_ex(Response1, StepSize, Num_Lines, [25,30,35],
InterpType)
Defined in
Built in
93
Measurement Expressions
See Also
contour() (expmeas), contour_polar() (expmeas)
Notes/Equations
This function is an extended function for contour() and contour_polar(). It generates
contours at desired levels that you specify, or at "round number" values on polar, or
rectangular surface data.
contour()
Generates contour levels on surface data
Syntax
y = contour(data, contour_levels, interpolation_type)
Arguments
Name
Description
Default
Range Type
Required
data
data to be contoured, which
must be at least twodimensional real, integer or
implicit
None
(-∞:∞) Integer,
Real
Yes
contour_levels
one-dimensional quantity
specifying the levels of the
contours †
six levels equally spaced
(-∞:∞) Integer,
between the maximum and
Real
the minimum of the data
No
0
No
interpolation_type specifies the type of
interpolation to perform
[0,1,2] Integer
††
† Normally specified by the sweep generator "[ ]," but can also be specified as a vector
† † Interpolation types are: 0 - No Interpolation,1 - Cubic Spline,2 - B-Spline
Examples
a = contour(dB(S11), [1::3::10])
a = contour(dB(S11), {1, 4, 7, 10})
produces a set of four equally spaced contours on a surface generated as a
function of, say, frequency and strip width.
a = contour(dB(S11), {1, 4, 7, 10}, 1)
produces the same set of contours as the above example, but with cubic spline
interpolation.
Defined in
Built in
See Also
94
Measurement Expressions
contour_polar() (expmeas)
Notes/Equations
This function introduces three extra inner independents into the data. The first two are
"level", the contour level, and "number", the contour number. For each contour level there
may be n contours. The contour is an integer running from 1 to n. The contour is
represented as an (x, y) pair with x as the inner independent.
contour_polar()
Generates contour levels on polar or Smith chart surface data
Syntax
y = contour_polar(data, contour_levels, InterpolationType, DataFormat)
Arguments
Name
Description
Range
Type
Required
data
polar or Smith chart data to None
be contoured, (and
therefore is surface data)
(-∞:∞)
Integer,
Real,
Complex
Yes
contour_levels
one-dimensional quantity
specifying the levels of the
contours †
six levels equally spaced
(-∞:∞)
between the maximum and
the minimum of the data
Integer,
Real
No
InterpolationType specifies the type of
interpolation to perform
0
[0,1,2]
††
Integer
No
DataFormat
"RI"
"RI",
String
"MA" ††
format of swept data
Default
No
† Normally specified by the sweep generator "[ ]," but can also be specified as a vector
† † Interpolation types are: 0 - No Interpolation,1 - Cubic Spline,2 - B-Spline
†† DataFormat are: "RI" = real-imaginary, "MA" = magnitude-phase
Examples
a = contour_polar(data_polar, [1::4])
a = contour_polar(data_polar, {1, 2, 3, 4})
produces a set of four equally spaced contours on a polar or Smith chart
surface.
a = contour_polar(data_polar, {1, 2, 3, 4}, 2)
produces the same set of contours as the above example, but with B-spline
interpolation.
Defined in
$HPEESOF_DIR/expressions/ael/display_fun.ael
See Also
95
Measurement Expressions
contour() (expmeas)
Notes/Equations
This function introduces three extra inner independents into the data. The first two are
"level", the contour level, and "number", the contour number. For each contour level there
may be n contours. The contour is an integer running from 1 to n. The contour is
represented as an (x,y) pair with x as the inner independent.
copy()
Makes a copy of a multi-dimensional data variable
Syntax
y = copy(DataVar)
Arguments
Name
Description
DataVar data variable or array that is to be
copied
Default Range Type
Required
None
Yes
None
Boolean, integer, real, complex,
string
Examples
result = copy(S21) returns the copy of the data stored in the data variable S21
The array or data variable created above can be used as follows:
indepV = indep(result,"Index");
result[0] = complex(1, 2); Sets the first value to a complex number
indepV[0] = 1GHz;
Defined in
Built in
See Also
create() (expmeas), delete() (expmeas)
Notes/Equations
Makes a copy of a multi-dimensional data variable, so that the contents of the copy can be
manipulated. Data Variables in ADS are data structures that are used to hold multidimensional data. Internally they are not implemented as arrays, and therefore do not
have the performance of an array. Accessing and setting data in these arrays are
performance intensive and should be noted.
create()
Creates a multi-dimensional data variable
96
Measurement Expressions
Syntax
y = create(Dimensionality, DependDataType, IndepName, IndepType, NumRows,
NumColumns)
Arguments
Name
Description
Default Range Type
Required
Dimensionality
dimensionality of the data variable or
array
None
[1:∞)
Integer Yes
DependDataType Dependent data type
"Real"
†
String
No
IndepName
Name(s) of independent
"__i"
None
String
No
IndepType
Independent data type
"Real"
†
String
No
NumRows
Number of rows
0
[0:∞)
Integer No
NumColumns
Number of columns
0
[0:∞)
Integer No
† "Boolean", "Integer", "Real", "Complex", "String" or "Byte16"
Examples
result = create(1, "Complex", {"Index"}, {"Real"},1, 1) returns a 1 dimensional
data variable with dependent type Complex, independent name "Index" and type
real with 1 row and column
The array or data variable created above can be used as follows:
indepV = indep(result,"Index");
result[0] = 1.1;
indepV[0] = 1.0;
A 2-dimensional example is given in the Measurement Expression AEL function
below. Test the function by doing the following:
* Copy the code below into the file user_defined_fun.ael in the directory
$HOME/hpeesof/expressions/ael.
* Launch ADS. In a DDS window create an equation: cre2D=datavar_test_create2()
* Display cre2D to see the contents.
defun datavar_test_create2()
{
decl result = create(2, "Complex", {"Index1", "Index2"}, {"String", "Real"},1,
1);
decl idenp1V = indep(result, "Index1");
decl idenp2V = indep(result, "Index2");
decl iD1, iD2;
for (iD1=0; iD1 < 2; iD1++) {
for (iD2=0; iD2 < 3; iD2++) {
result[iD1,iD2] = complex(iD1, iD2);
idenp2V[iD2] = iD2;
} //for
idenp1V[iD1] = strcat("Val", iD1);
} //for
return result;
}
Defined in
97
Measurement Expressions
Defined in
Built in
See Also
copy() (expmeas), delete() (expmeas)
Notes/Equations
The create() function can only be used from the measurement expression AEL code and
not from the DDS, the schematic, or PDE AEL.
See the Examples section.
This function is used to create multi-dimensional data variable or arrays. Data Variables in
ADS are data structures that are used to hold multi-dimensional data. Internally they are
not implemented as arrays, and therefore do not have the performance of an array.
Accessing and setting data in these arrays are performance intensive and should be noted.
The number of rows and columns are used in specifying the dimension of matrix data. For
a scalar this would be 1, 1.
dd_threshold()
Returns the filtered S Parameter matrix
Syntax
S_Filtered = dd_threshold(S, rep_func, mod_func , relop,threshold,low_freq,high_freq)
Arguments
Name
Description
Default Range
Type
Required
S
the input S matrix that needs to be filtered
None
(-∞:∞)
Real,
Complex
Yes
rep_func a function that reduces linear data to scalar data
that can be compared with the threshold eg:
dd_rms,min
None
(-∞:∞)
function
Yes
mod_func a function that is used to modify the Sij data to
comparable units with the threshold eg: dB
None
(-∞:∞)
function
Yes
relop
">="
(">" , ">=" ,
"==", "!=" ,
"<=" ,"<")
String
Yes
threshold the rhs value for the relational operator
None
(-∞:∞)
Real
Yes
low_freq
None
(-∞)
Real
No
None
(∞)
Real
No
the relational operator, in double quotes as a
string, to compare the Sij statistic and the
threshold.: lhs = statistic rhs = threshold
lower bound for frequency
high_freq higher bound for freq
Examples
S_Filtered = dd_threshold(S, dd_rms,dB ,">=", -30.0,10 Hz, 8GHz).
Defined in
$HPEESOF_DIR/expressions/ael/utility_fun.ael
98
Measurement Expressions
See Also
find index() (expmeas), mix() (expmeas)
Notes/Equations
This function filteres out unwanted S parameters
This function can accept conditionals such as ==, !=, >, <, >= and <=, but not logical
operators such as && and ||.
delete()
Deletes the multi-dimensional data variable
Syntax
y = delete(DataVar)
Arguments
Name
Description
DataVar data variable or array that is to be
deleted
Default Range Type
Required
None
Yes
None
Boolean, integer, real, complex,
string
Examples
result = delete(S21) returns true or false depending on whether the data
variable was deleted or not
Defined in
Built in
See Also
copy() (expmeas), create() (expmeas)
expand()
Expands the dependent data of a variable into single points by introducing an additional
inner independent variable
Syntax
y = expand(x)
Arguments
Name Description
x
Default Range Type
data to be expanded (dimension is larger than one and None
less than four)
(∞:∞)
Examples
Given a dependent data A which has independent variables
99
Integer, real,
Complex
Required
Yes
Measurement Expressions
B: If A is a 1 dimensional data containing 4 points (10, 20, 30, and 40) and
similarly B is made up of 4 points (1, 2, 3, and 4),
Eqn A = [10,20,30,40]
Eqn B = [1,2,3,4]
Eqn C = vs(A,B,"X")
Using expand(C) increases the dimensionality of the data by 1 where each inner
dependent variable ("X") consists of 1 point.
Eqn Y = expand(C)
X
C
A
B
Y
1234 10203040 10203040 1234 X=1 10X=2 20X=3 30X=4 40
Defined in
Built in
See Also
collapse() (expmeas)
Notes/Equations
In addition to the application above, the expand() function can also be used to convert a
matrix into an array or vector. For example, an S-parameter matrix can be converted into
an array by using the equation arr=expand(S) .
find()
Finds the indices of the conditions that are true. Use with all simulation data
Syntax
indices = find(condition)
Arguments
Name
Description Default Range Type Required
condition condition
None
None
string Yes
Examples
Given an S-parameter data swept as a function of frequency, find the value of
S11 at 1GHz:
index_1 = find(freq == 1GHz)
data = S11[index_1]
Given an S-parameter data swept as a function of frequency, find the values of
the frequencies where the
magnitude of S11 is greater than a given value.
lookupValue = 0.58
indices = find(mag(S11) > lookupValue))
100
Measurement Expressions
firstPoint = indices[0]
lastPoint = indices[sweep_size(indices)-1]
freqDifference = freq[lastPoint]- freq[firstPoint]
The following examples assume a Harmonic Balance data vtime, and a marker m1.
Find the dependent value at the marker:
vVal = find(indep(vtime) >= indep(m1) && indep(vtime) <= indep(m1))
Find all the dependent values less than that of the m1 or the value at m1:
vVal = find(indep(vtime) < indep(m1) ,, indep(vtime) == indep(m1))
Find all the dependent values that are not equal to m1:
vVal = find(indep(vtime) != indep(m1))
Defined in
$HPEESOF_DIR/expressions/ael/utility_fun.ael
See Also
find_index() (expmeas), mix() (expmeas)
Notes/Equations
The find function will return all the indices of the conditions that are true. If none of the
conditions are true, then a -1 is returned. The find function performs an exhaustive search
on the given data. The supplied data can be an independent or dependent data. In
addition, the dimension of the data that is returned will be identical to the dimension of
the input data.
The find function can accept conditionals such as ==, !=, >, <, >= and <=, and logical
operators such as && and ||.
find_index()
Finds the closest index for a given search value. Use with all simulation data
Syntax
index = find_index(data_sweep, search_value)
Arguments
Name
Description
data_sweep
data to search None
search_value value to
search
Default Range Type
None
Required
(∞:∞)
Integer, Real, complex,
string
Yes
(∞:∞)
Integer, Real, complex,
string
Yes
Examples
Given S-parameter data swept as a function of frequency, find the value of S11 at 1 GHz:
index = find_index(freq, 1GHz)
101
Measurement Expressions
a = S11[index]
Defined in
Built in
See Also
find() (expmeas), mix() (expmeas)
Notes/Equations
To facilitate searching, the find_index function finds the index value in a sweep that is
closest to the search value. Data of type int or real must be monotonic. find_index also
performs an exhaustive search of complex and string data types.
Note
For a more robust and versatile data-search tool, see the find() (expmeas) function.
generate()
This function generates a sequence of real numbers. The modern way to do this is to use
the sweep generator "[ ]."
Syntax
y = generate(start, stop, npts)
Arguments
Name Description
Default Range Type
Required
start
start value of sequence
None
(∞:∞)
Integer,
real
Yes
stop
stop value of sequence
None
(∞:∞)
Integer,
real
Yes
npts
Numper of points in the sequence None
[2:∞)
Integer
Yes
Examples
a = generate(9, 4, 6) returns the sequence 9., 8., 7., 6., 5., 4
Defined in
$HPEESOF_DIR/expressions/ael/elementary_fun.ael
get_attr()
Gets a data attribute. This function only works with frequency swept variables.
102
Measurement Expressions
Syntax
y = get_attr(data, "attr_name", eval)
Arguments
Name
Description
Default Range
Type
data
frequency swept variable
None
(-∞:∞)
Integer, Real, Complex Yes
attr_name name of the attribute
None
None
string
eval
true
false,true boolean
specifies whether to evaluate the
attribute
Required
Yes
No
Examples
y = get_attr(data, "fc", true) returns 10GHz
y = get_attr(data, "dataType") returns "TimedData"
y = get_attr(data, "TraceType", false) returns "Spectral"
Defined in
Built in
See Also
set_attr() (expmeas)
get_indep_values()
Returns the independent values associated with the given dependent value as an array.
Syntax
indepVals = get_indep_values(Data, LookupValue)
Arguments
Name
Description
Default Range Type
Required
Data
1 to 5 dimensional array.
None
(∞:∞)
Integer, Real,
Complex
Yes
LookupValue Dependent value for which the corresponding
independent values have to be found.
None
(∞:∞)
Real, Complex
Yes
Tolerance
tolerance to be used while comparing numbers
0
[0:∞)
Real
No
All
Finds all matches of the LookupValue. Default
behavior is to return after the first match.
0
[0:1]
Integer
No
Examples
We assume that the data is 2-dimensional i.e. 2 independent variables created
from a Harmonic Balance Analysis with Pout being the output data.
indepVals = get_indep_values(Pout, max(max(Pout)) returns the values of the
indepenent as an array.
indepVals = get_indep_values(Pout, [m1,m2]) returns the indepenent values of
the markers m1 and m2.
103
Measurement Expressions
Defined in
$HPEESOF_DIR/expressions/ael/utility_fun.ael
See Also
indep() (expmeas)
Notes/Equations
This function can be used only on 1 to 5 dimensional data. The independent values have
to be real. The dependent value to be looked up can be a single value or multiple values.
indep()
Returns the independent attached to the data
Syntax
Y = indep(x, NumberOrName)
Arguments
Name
Description
Default Range Type
x
data to access the independent
values
None
(∞:∞)
Integer, Real, Complex Yes
0
[0:6]
Integer, string
NumberOrName number or name of independent
Required
No
Examples
Given S-parameters versus frequency and power: Frequency is the innermost
independent, so its index is 1. Power has index 2.
freq = indep(S, 1)
freq = indep(S, "freq")
power = indep(S, 2)
power = indep(S, "power")
Defined in
Built in
See Also
find_index() (expmeas), get_indep_values() (expmeas)
104
Measurement Expressions
Notes/Equations
The indep() function returns the independent (normally the swept variable) attached to
simulation data. When there is more than one independent, then the independent of
interest may be specified by number or by name. If no independent specifications are
passed, then indep() returns the innermost independent.
max_index()
Returns the index of the maximum
Syntax
max_index(x)
Arguments
Name Description
x
Default Range Type
data to find maximum index None
(∞:∞)
Integer, real or
complex
Required
Yes
Examples
y = max_index([1, 2, 3]) returns 2
y = max_index([3, 2, 1]) returns 0
Defined in
Built-in
See Also
min_index() (expmeas)
min_index()
Returns the index of the minimum
Syntax
y = min_index(x)
Arguments
Name Description
Default Range Type
Required
x
None
Yes
data to find the minimum
index
(∞:∞)
Integer, real or
complex
Examples
a = min_index([3, 2, 1]) returns 2
a = min_index([1, 2, 3]) returns 0
105
Measurement Expressions
Defined in
Built in
See Also
max_index() (expmeas)
permute()
Permutes data based on the attached independents
Syntax
y = permute(data, permute_vector)
Arguments
Name
Description
Default Range Type
Required
data
any N-dimensional square data (all inner
independents must have the same value N)
None
(∞:∞)
Integer, Real,
Complex
Yes
None
(∞:∞)
Integer, Real,
Complex
Yes
permute_vector any permutation vector of the numbers 1
through N †
† The permute_vector defaults to {N::1}, representing a complete reversal of the data
with respect to its independent variables. If permute_vector has fewer than N entries, the
remainder of the vector, representing the outer independent variables, is filled in. In this
way, expressions remain robust when outer sweeps are added
Examples
Lets assume that the variable data has 3 independent variables. Then:
a1 = permute(data)
reverses the (three inner independents of) the data.
a2 = permute(data, {3, 2, 1})
Same as above.
aOrig = permute(data, {1, 2, 3})
preserves the data.
In the example below lets assume that a DC analysis has been done with two
independent variables VGS and VDS, and IDS.i is the dependent variable. To see
a plot of IDS vs VGS for different values of VDS the data can be permuted as
follows:
permutedData=permute(IDS.i,{2,1})
See the example $HPEESOF_DIR/examples/Tutorial/sweep.dds
Defined in
Built in
106
Measurement Expressions
See Also
plot_vs() (expmeas)
Notes/Equations
The permute() function is used to swap the order of the independent variables that are
attached to a data variable. For example, a data could have two independent variables in
a particular order. To swap the order so that it can be easily plotted, the order of the
independents must be swapped. The permute() function can be used for this purpose.
The permute() function cannot be used to swap the rows and columns of a matrix.
However, it can be used to swap the orders of the independent, even if the dependent is a
matrix. For example, a parameter sweep of an S-parameter analysis.
plot_vs()
Attaches an independent to data for plotting
Syntax
y = plot_vs(dependent, independent)
Arguments
Name
Description
Default Range Type
Required
dependent
any N-dimensional square data (all inner
independents must have the same value N)
None
(∞:∞)
Integer, Real,
Complex
Yes
None
(∞:∞)
Integer, Real
Yes
independent independent variable
Examples
Example 1:
a=[1, 2, 3]
b=[4, 5, 6]
c=plot_vs(a, b)
Builds c with independent b, and dependent a.
Example 2:
Assume that an S-parameter analysis has been done with one swept variable Cval
(of say 10 values) for 20 frequency points. The dependent data dbS11=db(S11) is
of 2 dimension and Dependency of [10, 20]. A standard plot would display dbS11
vs freq(the inner independent), for 10 values of Cval. Instead to plot dbS11 vs
Cval, the plot_vs() function can used as follows:
plot_vs(dbS11, Cval)
To plot dbS11 for half the values of Cval:
CvalH=Cval/2
plot_vs(dbS11, CvalH)
Example 3:
In the example below lets assume that a DC analysis has been done with two
independent variables Vgs and Vds, and Ids.i is the dependent variable. To see
a plot of Ids vs Vgs for different values of Vds the data can be plotted as
107
Measurement Expressions
follows:
plot_vs(Ids.i, Vgs)
Defined in
$HPEESOF_DIR/expressions/ael/display_fun.ael
See Also
indep() (expmeas), permute() (expmeas), vs() (expmeas)
Notes/Equations
When using plot_vs(), the independent and dependent data should be the same size (i.e.,
not irregular). This function works as follows:
Checks to see if the argument "independent", is an independent of argument
"depend" or argument "independent" is dis-similar to independent of argument
"depend".
If one of the above conditions is met, then the data is swapped or sliced, and the
new result formed with the argument "independent" is returned.
set_attr()
Sets the data attribute
Syntax
y = set_attr(data, "attr_name", attribute_value)
Arguments
Name
Description
Default Range Type
Required
data
data
None
(∞:∞)
Integer, Real, Complex
Yes
attr_name
name of the
attribute
None
None
string
Yes
(∞:∞)
boolean, integer, real, complex Yes
attribute_value value of the attribute None
Examples
a = set_attr(data, "TraceType", "Spectral")
a = set_attr(data, "TraceType", "Histogram")
Defined in
Built in
108
Measurement Expressions
Notes: When a variable's attributes are set using set_attr, any other equations using that
variable are not re-evaluated.
See Also
get_attr() (expmeas)
size()
Returns the row and column size of a vector or matrix
Syntax
y = size(x)
Arguments
Name Description Default Range Type
x
data
None
(∞:∞)
Required
Integer, Real, Complex Yes
Examples
Given 2-port S-parameters versus frequency, and given 10 frequency points. Then
for ten 2 2 matrices, size() returns the dimensions of the S-parameter matrix,
and its companion function sweep_size() returns the size of the sweep:
Y = size(S) returns {2, 2}
Y = sweep_size(S) returns 10
Defined in
Built in
See Also
sweep_size() (expmeas)
sort()
This measurement returns a sorted variable in ascending or descending order. The sorting
can be done on the independent or dependent variables. String values are sorted by
folding them to lower case.
Syntax
y = sort(data, sortOrder, indepName)
Arguments
109
Measurement Expressions
Name
Description
data
sortOrder
Default
Range
Type
data to be sorted
None
(multidimensional scalar variable)
(-∞:∞)
Integer, real or Yes
complex
sorting order
"ascending"
"ascending" or
"descending"
string
No
dependent
value †
None
string
No
indepName specify the name of the
independent variable for sorting
† if indepName not specified, the sorting is done on the dependent.
Examples
a = sort(data)
a = sort(data, "descending", "freq")
Defined in
Built in
sweep_dim()
Returns the dimensionality of the data
Syntax
y = sweep_dim(x)
Arguments
Name Description Default Range Type
x
data
None
(∞:∞)
Required
Integer, Real, Complex Yes
Examples
a = sweep_dim(1) returns 0
a = sweep_dim([1, 2, 3]) returns 1
Defined in
Built in
See Also
sweep_size() (expmeas)
sweep_size()
Returns the sweep size of a data object
Syntax
y = sweep_size(x)
110
Required
Measurement Expressions
Arguments
Name Description Default Range Type
x
data
None
(∞:∞)
Required
Integer, Real, Complex Yes
Examples
Given 2-port S-parameters versus frequency, and given 10 frequency points,
there are then ten 2 X 2 matrices. sweep_size() is used to return the sweep
size of the S-parameter matrix, and its companion function size() returns the
dimensions of the S-parameter matrix itself:
a = sweep_size(S) returns 10
a = size(S) returns {2, 2}
Irregular data:
Assume that the data is 3 dimensional with the last dimension being irregular.
The independents are: Vsrc, size, time with dimension [3,2,irreg]. Then:
SwpSz=sweep_size(data) would return:
__SIZE SwpSz
Vsrc=1.0,size=1.0
1 20
Vsrc=1.0,size=2.0
1 21
Vsrc=2.0,size=1.0
1 59
Vsrc=2.0,size=2.0
1 61
Vsrc=3.0,size=1.0
1 76
Vsrc=3.0,size=2.0
1 78
where __SIZE is an independent added by the sweep_size() function.
sweep_size(SwpSz) would return the correct size of the two outer variables:
(1) (2) (3)
3 2 1
Defined in
Built in
See Also
size() (expmeas), sweep_dim() (expmeas)
Notes/Equations
For regular data, this function returns a vector with an entry corresponding to the length
of each sweep. For irregular data, the function returns a multi-dimensional data, which
needs to be processed further to get the size. See example above.
111
Measurement Expressions
type()
Returns the type of the data.
Syntax
y = type(x)
Arguments
Name Description
x
Default Range Type
data to find the type None
(∞:∞)
Required
Integer, Real, Complex, String Yes
Examples
a
a
a
a
=
=
=
=
type(1) returns "Integer"
type(1.1) returns "Real"
type(1i) returns "Complex"
type("type") returns "String"
Defined in
Built in
See Also
what() (expmeas)
vs()
Attaches an independent to dependent data
Syntax
y = vs(dependent, independent, indepName)
Arguments
Name
Description
Default Range Type
Required
dependent
dependent values
None
(∞:∞)
Integer, real
Yes
independent independent values None
(∞:∞)
Integer, real, string, complex Yes
indepName independent name None
None
string
No
Examples
a=[1, 2, 3]
b=[4, 5, 6]
c = vs(a, b)
112
Measurement Expressions
Defined in
Built in
See Also
indep() (expmeas), plot_vs() (expmeas)
Notes/Equations
Use the plot_vs() function to plot the dependent with the order of independent changed.
For example, to plot Ids vs Vgs, in a DC analysis data with two independent variables, Vgs
and Vds, and a dependent variable Ids.i, use as below:
plot_vs(Ids.i, Vgs)
what()
Returns size and type of data
Syntax
y = what(x, DisplayBlockName)
Arguments
Name
Description
Default Range Type
x
data
None
(∞:∞)
0
[0:1] † Integer
DisplayBlockName Displays block
name
Required
Integer, Real, Complex, String Yes
No
† If DisplayBlockName equals 0, no block name is specified (default behavior). If
DisplayBlockName equals 1, then block name is displayed. If DisplayBlockName is not
equal to 0 or 1, it defaults to 0.
Examples
x=[10,20,30,40]
y=what(x)
returns:
y
Dependency : [ ]
Num. Points : [4]
Matrix Size : scalar
Type : Integer
y=what(x, 1)
returns:
y
Dependency : [ ]
Num. Points : [4]
Matrix Size : scalar
Type : Integer
Block Name: __tmp_XX
113
Measurement Expressions
Defined in
Built in
See Also
type() (expmeas)
Notes/Equations
This function is used to determine the dimensions of a piece of data, the attached
independents, the type, and (in the case of a matrix) the number of rows and columns.
Use what() by entering a listing column and using the trace expression what(x).
write_var()
Writes dataset variables to a file
Syntax
y = write_var(FileName, WriteMode, Comment, Delimiter, Format, Precision, Var1,
Var2,...,VarN)
Arguments
Name
Description
Default Range
Type
Required
FileName
Name of the output file
None
None
String
Yes
WriteMode
Describes the write mode - overwrite or
append
None
"W","A" † String
Yes
Comment
Text to be written at the top of the file
""
None
String
No
Delimiter
Delimiter that separates the data
"\t"
None
String
No
Format
Format of the data
"f"
"f","s" †† String
No
Precision
precision of the data
6
[1:64]
Integer
No
None
None
dataset
variable
Yes
Var1,...,VarN Data variables to be written
† WriteMode: "W" - overwrite the file, "A" - append to the file
†† Format: "f" - full notation, "s" - scientific notation
Examples
write_var_f=write_var("output_S21.txt","W","! Freq real(S21) imag(S21)"," ",,
14, freq, S21)
writes S21 to the output file output_S21.txt as:
! Freq real(S21) imag(S21)
1000000000 0.60928892074273 -0.10958342264718
2000000000 0.52718867597783 -0.13319167002392
3000000000 0.4769067837712 -0.12080489345341
wv_ib=write_var("output_hbIb.txt","W","! HB Ib.i", " ",,,freq, Ib.i)
114
Measurement Expressions
write the Harmonic Balance frequency and current Ib.i to the output file
output_hbIb.txt.
Defined in
$HPEESOF_DIR/expressions/ael/utility_fun.ael
See Also
indep() (expmeas)
Notes/Equations
This function can be used to write multiple dataset variables to a file. Currently only 1
dimensional data is supported. All variables that are to be written must be of the same
size. Each variable data is written in column format. Complex data type is written in 2
columns as real and imaginary.
115
Measurement Expressions
FrontPanel Eye Diagram Functions
This section describes the eye diagram FrontPanel and associated functions in detail.
These functions are not generalized functions, they are provided specifically to support the
eye diagram utility available from the Data Display.
eye binning() (expmeas)
eye density() (expmeas)
FrontPanel eye 2d indepvar maximum inner() (expmeas)
FrontPanel eye() (expmeas)
FrontPanel eye amplitude histogram() (expmeas)
FrontPanel eye crossings() (expmeas)
FrontPanel eye delay() (expmeas)
FrontPanel eye fall trace() (expmeas)
FrontPanel eye horizontal histogram() (expmeas)
FrontPanel eye regular() (expmeas)
FrontPanel eye risefall marker() (expmeas)
FrontPanel eye rise trace() (expmeas)
FrontPanel eye topbase() (expmeas)
FrontPanel get histogram mean stddev() (expmeas)
FrontPanel pp rms jitter() (expmeas)
FrontPanel wave 1st falling edge period() (expmeas)
FrontPanel wave 1st rising edge period() (expmeas)
FrontPanel wave 1st transition fall time() (expmeas)
FrontPanel wave 1st transition rise time() (expmeas)
FrontPanel wave datarate() (expmeas)
FrontPanel wave negative pulse width() (expmeas)
FrontPanel wave positive pulse width() (expmeas)
FrontPanel wave topbase() (expmeas)
Working with the Eye Diagram FrontPanel
The eye diagram FrontPanel is available from the Data Display Tools > Eye Diagram
menu. The FrontPanel features two modes of operation: oscilloscope and eye/mask . For
more information on working with the eye diagram FrontPanel, refer to the Data Display
documentation.
eye_binning()
Returns density binning data
Syntax
y = eye_binning(eye_data, Indep_bins, Dep_bins)
Arguments
116
Measurement Expressions
Name
Description
Default Range Type
Required
eye_data
eye diagram data
None
(∞:∞)
Real
Yes
Indep_bins number of independent bins None
[1:∞)
Integer Yes
Dep_bins
[1:∞)
Integer Yes
number of dependent bins
None
Examples
Eye_data=FrontPanel_eye(vout,10GHz)
Eye_bins = eye_binning(Eye_data, 100, 70);
Defined in
$HPEESOF_DIR/expressions/ael/DesignGuide_fun.ael
See Also
eye() (expmeas), eye_density() (expmeas), FrontPanel_eye() (expmeas),
FrontPanel_eye_2d_indepvar_maximum_inner() (expmeas),
FrontPanel_eye_amplitude_histogram() (expmeas), FrontPanel_eye_crossings()
(expmeas), FrontPanel_eye_delay() (expmeas), FrontPanel_eye_fall_trace() (expmeas),
FrontPanel_eye_horizontal_histogram() (expmeas), FrontPanel_eye_regular() (expmeas),
FrontPanel_eye_rise_trace() (expmeas), FrontPanel_eye_risefall_marker() (expmeas),
FrontPanel_eye_topbase() (expmeas), FrontPanel_get_histogram_mean_stddev()
(expmeas), FrontPanel_pp_rms_jitter() (expmeas),
FrontPanel_wave_1st_falling_edge_period() (expmeas),
FrontPanel_wave_1st_rising_edge_period() (expmeas),
FrontPanel_wave_1st_transition_fall_time() (expmeas),
FrontPanel_wave_1st_transition_rise_time() (expmeas), FrontPanel_wave_datarate()
(expmeas), FrontPanel_wave_negative_pulse_width() (expmeas),
FrontPanel_wave_positive_pulse_width() (expmeas), FrontPanel_wave_topbase()
(expmeas)
Notes/Equations
This function takes a multi-dimensional eye diagram plot and performs binning. The
binning is performed by slicing the eye diagram on its X-axis (Indep_bins) and Y-axis
(Dep_bins) and returning number of traces passing through every bin. The eye binning
information can be used to calculate trace distribution in any region of the eye diagram.
eye_density()
Returns density trace.
Syntax
y = eye_density(eye_data, Indep_bins, Dep_bins)
Arguments
117
Measurement Expressions
Name
Description
Default Range Type
Required
eye_data
eye diagram data
None
(∞:∞)
Real
Yes
Indep_bins number of independent bins None
[1:∞)
Integer Yes
Dep_bins
[1:∞)
Integer Yes
number of dependent bins
None
Examples
Eye_data=FrontPanel_eye(vount,10GHz)
Eye_bins = eye_density(Eye_data, 100, 70);
Defined in
$HPEESOF_DIR/expressions/ael/DesignGuide_fun.ael
See Also
eye() (expmeas), eye_binning() (expmeas), FrontPanel_eye() (expmeas),
FrontPanel_eye_2d_indepvar_maximum_inner() (expmeas),
FrontPanel_eye_amplitude_histogram() (expmeas), FrontPanel_eye_crossings()
(expmeas), FrontPanel_eye_delay() (expmeas), FrontPanel_eye_fall_trace() (expmeas),
FrontPanel_eye_horizontal_histogram() (expmeas), FrontPanel_eye_regular() (expmeas),
FrontPanel_eye_rise_trace() (expmeas), FrontPanel_eye_risefall_marker() (expmeas),
FrontPanel_eye_topbase() (expmeas), FrontPanel_get_histogram_mean_stddev()
(expmeas), FrontPanel_pp_rms_jitter() (expmeas),
FrontPanel_wave_1st_falling_edge_period() (expmeas),
FrontPanel_wave_1st_rising_edge_period() (expmeas),
FrontPanel_wave_1st_transition_fall_time() (expmeas),
FrontPanel_wave_1st_transition_rise_time() (expmeas), FrontPanel_wave_datarate()
(expmeas), FrontPanel_wave_negative_pulse_width() (expmeas),
FrontPanel_wave_positive_pulse_width() (expmeas), FrontPanel_wave_topbase()
(expmeas)
FrontPanel_eye_2d_indepvar_maximum_inner()
Given two dimensional data, returns maximum value of the inner indpendent variable
Syntax
y = FrontPanel_eye_2d_indepvar_maximum_inner(eye_bin_data)
Arguments
Name
Description
Default Range Type Required
eye_bin_data eye binning data None
(∞:∞)
real
Yes
Examples
maximum_indep=FrontPanel_eye_2d_indepvar_maximum_inner(eye_bin_data)
118
Measurement Expressions
Defined in
$HPEESOF_DIR/expressions/ael/FrontPanel_fun.ael
See Also
eye_binning() (expmeas), eye_density() (expmeas), FrontPanel_eye() (expmeas),
FrontPanel_eye_amplitude_histogram() (expmeas), FrontPanel_eye_crossings()
(expmeas), FrontPanel_eye_delay() (expmeas), FrontPanel_eye_fall_trace() (expmeas),
FrontPanel_eye_horizontal_histogram() (expmeas), FrontPanel_eye_regular() (expmeas),
FrontPanel_eye_rise_trace() (expmeas), FrontPanel_eye_risefall_marker() (expmeas),
FrontPanel_eye_topbase() (expmeas), FrontPanel_get_histogram_mean_stddev()
(expmeas), FrontPanel_pp_rms_jitter() (expmeas),
FrontPanel_wave_1st_falling_edge_period() (expmeas),
FrontPanel_wave_1st_rising_edge_period() (expmeas),
FrontPanel_wave_1st_transition_fall_time() (expmeas),
FrontPanel_wave_1st_transition_rise_time() (expmeas), FrontPanel_wave_datarate()
(expmeas), FrontPanel_wave_negative_pulse_width() (expmeas),
FrontPanel_wave_positive_pulse_width() (expmeas), FrontPanel_wave_topbase()
(expmeas)
Notes/Equations
The FrontPanel_eye_2d_indepvar_maximum_inner() function essentially takes two
dimensional binning data and returns maximum value of inner independent variable.
FrontPanel_eye()
Creates data for an eye diagram plot with one bit shift per trace, adding an additional
cycle to the number of cycles defined
Syntax
y = FrontPanel_eye(NRZ_data, symbolRate, Cycles, Delay)
Arguments
Name
Description
Default Range Type
Required
NRZ_data
either numeric data or a time domain waveform,
typically NRZ data
None
(∞:∞)
Complex
Yes
symbolRate bit rate of the channel
None
(0:∞)
Real
Yes
Cycles
number of cycles to repeat
1
[1:∞)
Integer
No
Delay
sampling delay
0
[0:∞)
Integer,
Real
No
Examples
y = FrontPanel_eye(NRZ_data, symbol_rate)
Defined in
119
Measurement Expressions
Built in
See Also
eye_binning() (expmeas), eye_density() (expmeas),
FrontPanel_eye_2d_indepvar_maximum_inner() (expmeas),
FrontPanel_eye_amplitude_histogram() (expmeas), FrontPanel_eye_crossings()
(expmeas), FrontPanel_eye_delay() (expmeas), FrontPanel_eye_fall_trace() (expmeas),
FrontPanel_eye_horizontal_histogram() (expmeas), FrontPanel_eye_regular() (expmeas),
FrontPanel_eye_rise_trace() (expmeas), FrontPanel_eye_risefall_marker() (expmeas),
FrontPanel_eye_topbase() (expmeas), FrontPanel_get_histogram_mean_stddev()
(expmeas), FrontPanel_pp_rms_jitter() (expmeas),
FrontPanel_wave_1st_falling_edge_period() (expmeas),
FrontPanel_wave_1st_rising_edge_period() (expmeas),
FrontPanel_wave_1st_transition_fall_time() (expmeas),
FrontPanel_wave_1st_transition_rise_time() (expmeas), FrontPanel_wave_datarate()
(expmeas), FrontPanel_wave_negative_pulse_width() (expmeas),
FrontPanel_wave_positive_pulse_width() (expmeas), FrontPanel_wave_topbase()
(expmeas)
Notes/Equations
This function will shift the eye trace by one bit when multiple eyes are plotted as opposed
to eye() function.
FrontPanel_eye_amplitude_histogram()
Returns amplitude histogram from binning data
Syntax
y = FrontPanel_eye_amplitude_histogram(data)
Arguments
Name Description
Default Range Type Required
data
None
Eye binning data, usually the output of eye_binning
function
(∞:∞)
Examples
Find_hist = FrontPanel_eye_amplitude_histogram(eye_bin_data)
Defined in
$HPEESOF_DIR/expressions/ael/FrontPanel_fun.ael
See Also
120
Real Yes
Measurement Expressions
eye_binning() (expmeas), eye_density() (expmeas), FrontPanel_eye() (expmeas),
FrontPanel_eye_2d_indepvar_maximum_inner() (expmeas), FrontPanel_eye_crossings()
(expmeas), FrontPanel_eye_delay() (expmeas), FrontPanel_eye_fall_trace() (expmeas),
FrontPanel_eye_horizontal_histogram() (expmeas), FrontPanel_eye_regular() (expmeas),
FrontPanel_eye_rise_trace() (expmeas), FrontPanel_eye_risefall_marker() (expmeas),
FrontPanel_eye_topbase() (expmeas), FrontPanel_get_histogram_mean_stddev()
(expmeas), FrontPanel_pp_rms_jitter() (expmeas),
FrontPanel_wave_1st_falling_edge_period() (expmeas),
FrontPanel_wave_1st_rising_edge_period() (expmeas),
FrontPanel_wave_1st_transition_fall_time() (expmeas),
FrontPanel_wave_1st_transition_rise_time() (expmeas), FrontPanel_wave_datarate()
(expmeas), FrontPanel_wave_negative_pulse_width() (expmeas),
FrontPanel_wave_positive_pulse_width() (expmeas), FrontPanel_wave_topbase()
(expmeas)
Notes/Equations
The FrontPanel_eye_amplitude_histogram() function calculates the amplitude histogram
from eye binning data.
FrontPanel_eye_crossings()
Given lower boundary, top boundary and the data type returns the eye crossing points
Syntax
y = FrontPanel_eye_crossings(data,base_upper,top_lower,data_type)
Arguments
Name
Description
Default Range Type Required
data
eye binning data
None
(∞:∞)
real
base_upper upper three sigma point of the base boundary
None
(∞:∞)
Real Yes
top_lower
lower three sigma point of the top boundary
None
(∞:∞)
Real Yes
data_type
data type, current version supports only "NRZ"
data
None
String
Yes
Yes
Examples
Eye_crossing_array = FrontPanel_eye_crossings(eye_bin_data,0.2,0.8,"NRZ")
Eye_crossing_1_level=Eye_crossing_array[0]
Eye_crossing_1_time=Eye_crossing_array[1]
Eye_crossing_2_level=Eye_crossing_array[3]
Eye_crossing_2_time=Eye_crossing_array[4]
Defined in
$HPEESOF_DIR/expressions/ael/FrontPanel_fun.ael
See Also
121
Measurement Expressions
See Also
eye_binning() (expmeas), eye_density() (expmeas), FrontPanel_eye() (expmeas),
FrontPanel_eye_2d_indepvar_maximum_inner() (expmeas),
FrontPanel_eye_amplitude_histogram() (expmeas), FrontPanel_eye_delay() (expmeas),
FrontPanel_eye_fall_trace() (expmeas), FrontPanel_eye_horizontal_histogram()
(expmeas), FrontPanel_eye_regular() (expmeas), FrontPanel_eye_rise_trace()
(expmeas), FrontPanel_eye_risefall_marker() (expmeas), FrontPanel_eye_topbase()
(expmeas), FrontPanel_get_histogram_mean_stddev() (expmeas),
FrontPanel_pp_rms_jitter() (expmeas), FrontPanel_wave_1st_falling_edge_period()
(expmeas), FrontPanel_wave_1st_rising_edge_period() (expmeas),
FrontPanel_wave_1st_transition_fall_time() (expmeas),
FrontPanel_wave_1st_transition_rise_time() (expmeas), FrontPanel_wave_datarate()
(expmeas), FrontPanel_wave_negative_pulse_width() (expmeas),
FrontPanel_wave_positive_pulse_width() (expmeas), FrontPanel_wave_topbase()
(expmeas)
Notes/Equations
The FrontPanel_eye_crossings() function essentially takes the eye binning data, the top
and base boundary limits, and the data type, and returns crossing points as an array.
FrontPanel_eye_delay()
Returns delay required for eye pattern positioning
Syntax
y = FrontPanel_eye_delay(Vout_time,BitRate)
Arguments
Name
Description
Default Range Type Required
Vout_time time domain voltage waveform
BitRate
None
(∞:∞)
Real Yes
bit rate of the channel and is expressed in frequency units None
[0:∞)
Real Yes
Examples
Find_delay = FrontPanel_eye_delay(vout,1e9)
Defined in
$HPEESOF_DIR/expressions/ael/FrontPanel_fun.ael
See Also
eye_binning() (expmeas), eye_density() (expmeas), FrontPanel_eye() (expmeas),
FrontPanel_eye_2d_indepvar_maximum_inner() (expmeas),
FrontPanel_eye_amplitude_histogram() (expmeas), FrontPanel_eye_crossings()
(expmeas), FrontPanel_eye_fall_trace() (expmeas),
122
Measurement Expressions
FrontPanel_eye_horizontal_histogram() (expmeas), FrontPanel_eye_regular() (expmeas),
FrontPanel_eye_rise_trace() (expmeas), FrontPanel_eye_risefall_marker() (expmeas),
FrontPanel_eye_topbase() (expmeas), FrontPanel_get_histogram_mean_stddev()
(expmeas), FrontPanel_pp_rms_jitter() (expmeas),
FrontPanel_wave_1st_falling_edge_period() (expmeas),
FrontPanel_wave_1st_rising_edge_period() (expmeas),
FrontPanel_wave_1st_transition_fall_time() (expmeas),
FrontPanel_wave_1st_transition_rise_time() (expmeas), FrontPanel_wave_datarate()
(expmeas), FrontPanel_wave_negative_pulse_width() (expmeas),
FrontPanel_wave_positive_pulse_width() (expmeas), FrontPanel_wave_topbase()
(expmeas)
Notes/Equations
The FrontPanel_eye_delay() function determines eye mid crossing point of NRZ data and
calculates the delay required to position 50% eye crossing at the center of unit interval.
FrontPanel_eye_fall_trace()
Returns eye falling edges
Syntax
y = FrontPanel_eye_fall_trace(eye_bin_data, level_zero, level_one, low_threshold,
high_threshold)
Arguments
Name
Description
Default Range Type Required
eye_bin_data
eye binning data
None
(∞:∞)
real
level_zero
logic level zero amplitude None
(∞:∞)
Real Yes
level_one
logic level one amplitude
None
(∞:∞)
Real Yes
low_threshold low threshold percentage None
(∞:∞)
Real Yes
high_threshold high threshold precentage None
(∞:∞)
Real Yes
Yes
Examples
Eye_falling_traces = FrontPanel_eye_fall_trace(eye_bin_data,0,1.8, 10, 90)
Defined in
$HPEESOF_DIR/expressions/ael/FrontPanel_fun.ael
See Also
eye_binning() (expmeas), eye_density() (expmeas), FrontPanel_eye() (expmeas),
123
Measurement Expressions
FrontPanel_eye_2d_indepvar_maximum_inner() (expmeas),
FrontPanel_eye_amplitude_histogram() (expmeas), FrontPanel_eye_crossings()
(expmeas), FrontPanel_eye_delay() (expmeas), FrontPanel_eye_horizontal_histogram()
(expmeas), FrontPanel_eye_regular() (expmeas), FrontPanel_eye_rise_trace()
(expmeas), FrontPanel_eye_risefall_marker() (expmeas), FrontPanel_eye_topbase()
(expmeas), FrontPanel_get_histogram_mean_stddev() (expmeas),
FrontPanel_pp_rms_jitter() (expmeas), FrontPanel_wave_1st_falling_edge_period()
(expmeas), FrontPanel_wave_1st_rising_edge_period() (expmeas),
FrontPanel_wave_1st_transition_fall_time() (expmeas),
FrontPanel_wave_1st_transition_rise_time() (expmeas), FrontPanel_wave_datarate()
(expmeas), FrontPanel_wave_negative_pulse_width() (expmeas),
FrontPanel_wave_positive_pulse_width() (expmeas), FrontPanel_wave_topbase()
(expmeas)
Notes/Equations
The FrontPanel_eye_fall_trace() function essentially takes the eye binning data and
returns the falling edges which crosses the lower and upper threshold points.
FrontPanel_eye_horizontal_histogram()
Given start, stop time and amplitude,returns horizontal histogram from the eye binning
data
Syntax
y=
FrontPanel_eye_horizontal_histogram(data,start_time,stop_time,start_amp,stop_amp)
Arguments
Name
Description
Default Range Type Required
data
eye binning data
None
(∞:∞)
real
start_time start time of horizontal histogram
None
(∞:∞)
Real Yes
stop_time stop time of horizontal histogram
None
(∞:∞)
Real Yes
start_amp start amplitude of horizontal histogram None
(∞:∞)
Real Yes
stop_amp start amplitude of horizontal histogram None
(∞:∞)
Real Yes
Yes
Examples
Eye_histogram = FrontPanel_eye_horizontal_histogram(eye_bin_data,0,10e-9, -0.1,
0.1)
Defined in
$HPEESOF_DIR/expressions/ael/FrontPanel_fun.ael
124
Measurement Expressions
See Also
eye_binning() (expmeas), eye_density() (expmeas), FrontPanel_eye() (expmeas),
FrontPanel_eye_2d_indepvar_maximum_inner() (expmeas),
FrontPanel_eye_amplitude_histogram() (expmeas), FrontPanel_eye_crossings()
(expmeas), FrontPanel_eye_delay() (expmeas), FrontPanel_eye_fall_trace() (expmeas),
FrontPanel_eye_regular() (expmeas), FrontPanel_eye_rise_trace() (expmeas),
FrontPanel_eye_risefall_marker() (expmeas), FrontPanel_eye_topbase() (expmeas),
FrontPanel_get_histogram_mean_stddev() (expmeas), FrontPanel_pp_rms_jitter()
(expmeas), FrontPanel_wave_1st_falling_edge_period() (expmeas),
FrontPanel_wave_1st_rising_edge_period() (expmeas),
FrontPanel_wave_1st_transition_fall_time() (expmeas),
FrontPanel_wave_1st_transition_rise_time() (expmeas), FrontPanel_wave_datarate()
(expmeas), FrontPanel_wave_negative_pulse_width() (expmeas),
FrontPanel_wave_positive_pulse_width() (expmeas), FrontPanel_wave_topbase()
(expmeas)
Notes/Equations
The FrontPanel_eye_horizontal_histogram() function essentially takes the eye binning
data and returns horizontal histogram between start and stop points.
FrontPanel_eye_regular()
Given eye data and the resolution, returns uniformally spaced eye data
Syntax
y = FrontPanel_eye_regular(eye_data,resolution_x)
Arguments
Name
Description
Default Range Type Required
eye_data
eye diagram data
None
(∞:∞)
real
Yes
resolution_x inner independent variable resolution None
(∞:∞)
real
Yes
Examples
eye_data=eye(vout,1GHz)
uniform_eye_data=FrontPanel_eye_regular(eye_data,450)
Defined in
$HPEESOF_DIR/expressions/ael/FrontPanel_fun.ael
See Also
125
Measurement Expressions
eye_binning() (expmeas), eye_density() (expmeas), FrontPanel_eye() (expmeas),
FrontPanel_eye_2d_indepvar_maximum_inner() (expmeas),
FrontPanel_eye_amplitude_histogram() (expmeas), FrontPanel_eye_crossings()
(expmeas), FrontPanel_eye_delay() (expmeas), FrontPanel_eye_fall_trace() (expmeas),
FrontPanel_eye_horizontal_histogram() (expmeas), FrontPanel_eye_rise_trace()
(expmeas), FrontPanel_eye_risefall_marker() (expmeas), FrontPanel_eye_topbase()
(expmeas), FrontPanel_get_histogram_mean_stddev() (expmeas),
FrontPanel_pp_rms_jitter() (expmeas), FrontPanel_wave_1st_falling_edge_period()
(expmeas), FrontPanel_wave_1st_rising_edge_period() (expmeas),
FrontPanel_wave_1st_transition_fall_time() (expmeas),
FrontPanel_wave_1st_transition_rise_time() (expmeas), FrontPanel_wave_datarate()
(expmeas), FrontPanel_wave_negative_pulse_width() (expmeas),
FrontPanel_wave_positive_pulse_width() (expmeas), FrontPanel_wave_topbase()
(expmeas)
Notes/Equations
The FrontPanel_eye_regular() function essentially takes eye data, and returns uniform
spaced data. The first and last trace of the eye diagram will be removed when using this
function.
FrontPanel_eye_risefall_marker()
Returns the threshold points from rising or falling edge data
Syntax
y = FrontPanel_eye_risefall_marker(data, level_zero, level_one, low_threshold,
high_threshold)
Arguments
Name
Description
Default Range Type Required
data
eye binning data
None
(∞:∞)
real
level_zero
logic level zero amplitude None
(∞:∞)
Real Yes
level_one
logic level one amplitude
None
(∞:∞)
Real Yes
low_threshold low threshold percentage None
(∞:∞)
Real Yes
high_threshold high threshold precentage None
(∞:∞)
Real Yes
Yes
Examples
Eye_rise_marker = FrontPanel_eye_risefall_marker(eye_bin_data,0,1.8, 10, 90)
Defined in
$HPEESOF_DIR/expressions/ael/FrontPanel_fun.ael
126
Measurement Expressions
See Also
eye_binning() (expmeas), eye_density() (expmeas), FrontPanel_eye() (expmeas),
FrontPanel_eye_2d_indepvar_maximum_inner() (expmeas),
FrontPanel_eye_amplitude_histogram() (expmeas), FrontPanel_eye_crossings()
(expmeas), FrontPanel_eye_delay() (expmeas), FrontPanel_eye_fall_trace() (expmeas),
FrontPanel_eye_horizontal_histogram() (expmeas), FrontPanel_eye_regular() (expmeas),
FrontPanel_eye_rise_trace() (expmeas), FrontPanel_eye_topbase() (expmeas),
FrontPanel_get_histogram_mean_stddev() (expmeas), FrontPanel_pp_rms_jitter()
(expmeas), FrontPanel_wave_1st_falling_edge_period() (expmeas),
FrontPanel_wave_1st_rising_edge_period() (expmeas),
FrontPanel_wave_1st_transition_fall_time() (expmeas),
FrontPanel_wave_1st_transition_rise_time() (expmeas), FrontPanel_wave_datarate()
(expmeas), FrontPanel_wave_negative_pulse_width() (expmeas),
FrontPanel_wave_positive_pulse_width() (expmeas), FrontPanel_wave_topbase()
(expmeas)
Notes/Equations
The FrontPanel_eye_risefall_marker() function essentially takes the eye binning data and
returns the gaussian mean position at lower threshold, 50% crossing, and upper threshold
crossing points as an array. The first element of the array will give the indepedent and
dependent value at the lower threshold, the second element will give the 50% crossing
point, and the third element will give the high threshold point.
FrontPanel_eye_rise_trace()
Returns eye rising edges
Syntax
y = FrontPanel_eye_rise_trace(data, level_zero, level_one, low_threshold,
high_threshold)
Arguments
Name
Description
Default Range Type Required
data
eye binning data
None
(∞:∞)
real
level_zero
logic level zero amplitude None
(∞:∞)
Real Yes
level_one
logic level one amplitude
None
(∞:∞)
Real Yes
low_threshold low threshold percentage None
(∞:∞)
Real Yes
high_threshold high threshold precentage None
(∞:∞)
Real Yes
Yes
Examples
Eye_rising_traces = FrontPanel_eye_rise_trace(eye_bin_data,0,1.8, 10, 90)
127
Measurement Expressions
Defined in
$HPEESOF_DIR/expressions/ael/FrontPanel_fun.ael
See Also
eye_binning() (expmeas), eye_density() (expmeas), FrontPanel_eye() (expmeas),
FrontPanel_eye_2d_indepvar_maximum_inner() (expmeas),
FrontPanel_eye_amplitude_histogram() (expmeas), FrontPanel_eye_crossings()
(expmeas), FrontPanel_eye_delay() (expmeas), FrontPanel_eye_fall_trace() (expmeas),
FrontPanel_eye_horizontal_histogram() (expmeas), FrontPanel_eye_regular() (expmeas),
FrontPanel_eye_risefall_marker() (expmeas), FrontPanel_eye_topbase() (expmeas),
FrontPanel_get_histogram_mean_stddev() (expmeas), FrontPanel_pp_rms_jitter()
(expmeas), FrontPanel_wave_1st_falling_edge_period() (expmeas),
FrontPanel_wave_1st_rising_edge_period() (expmeas),
FrontPanel_wave_1st_transition_fall_time() (expmeas),
FrontPanel_wave_1st_transition_rise_time() (expmeas), FrontPanel_wave_datarate()
(expmeas), FrontPanel_wave_negative_pulse_width() (expmeas),
FrontPanel_wave_positive_pulse_width() (expmeas), FrontPanel_wave_topbase()
(expmeas)
Notes/Equations
The FrontPanel_eye_rise_trace() function essentially takes the eye binning data and
returns the rising edges which crosses the lower and upper threshold points.
FrontPanel_eye_topbase()
Given lower boundary, top boundary and the data type returns the eye crossing points
Syntax
y=
FrontPanel_eye_topbase(data,eye_crossing_points,lower_threshold,upper_threshold,data_type)
Arguments
Name
Description
Default Range Type Required
data
eye binning data
None
(∞:∞)
real
eye_crossing_points array of eye crossing points, typically
FrontPanel_eye_crossings function returned value
None
(∞:∞)
Real Yes
lower_threshold
lower threshold point %
None
(∞:∞)
Real Yes
upper_threshold
upper threshold point %
None
(∞:∞)
Real Yes
data_type
data type, current version supports only "NRZ" data
None
String
Yes
Yes
Examples
eye_crossing_points=FrontPanel_eye_crossings(eye_bin_data,-1.0,1,0,"NRZ")
128
Measurement Expressions
eye_top_base =
FrontPanel_eye_topbase(eye_bin_data,eye_crossing_points,20,80,"NRZ")
Defined in
$HPEESOF_DIR/expressions/ael/FrontPanel_fun.ael
See Also
eye_binning() (expmeas), eye_density() (expmeas), FrontPanel_eye() (expmeas),
FrontPanel_eye_2d_indepvar_maximum_inner() (expmeas),
FrontPanel_eye_amplitude_histogram() (expmeas), FrontPanel_eye_crossings()
(expmeas), FrontPanel_eye_delay() (expmeas), FrontPanel_eye_fall_trace() (expmeas),
FrontPanel_eye_horizontal_histogram() (expmeas), FrontPanel_eye_regular() (expmeas),
FrontPanel_eye_rise_trace() (expmeas), FrontPanel_eye_risefall_marker() (expmeas),
FrontPanel_get_histogram_mean_stddev() (expmeas), FrontPanel_pp_rms_jitter()
(expmeas), FrontPanel_wave_1st_falling_edge_period() (expmeas),
FrontPanel_wave_1st_rising_edge_period() (expmeas),
FrontPanel_wave_1st_transition_fall_time() (expmeas),
FrontPanel_wave_1st_transition_rise_time() (expmeas), FrontPanel_wave_datarate()
(expmeas), FrontPanel_wave_negative_pulse_width() (expmeas),
FrontPanel_wave_positive_pulse_width() (expmeas), FrontPanel_wave_topbase()
(expmeas)
Notes/Equations
The FrontPanel_eye_topbase() function essentially takes the eye binning data, the
crossing points, the lower and upper threshold percentage value, and returned top and
base levels.
Frontpanel_get_histogram_mean_stddev()
Given histogram data computes mean and standard deviation values
Syntax
y = Frontpanel_get_histogram_mean_stddev(data,start_bin,stop_bin)
Arguments
Name
Description
Default Range Type Required
data
histogram data
None
(∞:∞)
real
Yes
None
(∞:∞)
real
Yes
stop_bin stop bin number None
(∞:∞)
real
Yes
start_bin start bin
number
Examples
histogram_statistics=Frontpanel_get_histogram_mean_stddev(histogram_data,10,100)
129
Measurement Expressions
histogram_mean=histogram_statistics[0]
histogram_stddev=histogram_statistics[1]
Defined in
$HPEESOF_DIR/expressions/ael/FrontPanel_fun.ael
See Also
eye_binning() (expmeas), eye_density() (expmeas), FrontPanel_eye() (expmeas),
FrontPanel_eye_2d_indepvar_maximum_inner() (expmeas),
FrontPanel_eye_amplitude_histogram() (expmeas), FrontPanel_eye_crossings()
(expmeas), FrontPanel_eye_delay() (expmeas), FrontPanel_eye_fall_trace() (expmeas),
FrontPanel_eye_horizontal_histogram() (expmeas), FrontPanel_eye_regular() (expmeas),
FrontPanel_eye_rise_trace() (expmeas), FrontPanel_eye_risefall_marker() (expmeas),
FrontPanel_eye_topbase() (expmeas), FrontPanel_pp_rms_jitter() (expmeas),
FrontPanel_wave_1st_falling_edge_period() (expmeas),
FrontPanel_wave_1st_rising_edge_period() (expmeas),
FrontPanel_wave_1st_transition_fall_time() (expmeas),
FrontPanel_wave_1st_transition_rise_time() (expmeas), FrontPanel_wave_datarate()
(expmeas), FrontPanel_wave_negative_pulse_width() (expmeas),
FrontPanel_wave_positive_pulse_width() (expmeas), FrontPanel_wave_topbase()
(expmeas)
Notes/Equations
The FrontPanel_get_histogram_mean_stddev() function essentially takes histogram data
and returns mean and standard deviation.
FrontPanel_pp_rms_jitter()
Given histogram data computes peak to peak jitter value and RMS jitter value
Syntax
y = FrontPanel_pp_rms_jitter(histogram_data)
Arguments
Name
Description
Default Range Type Required
histogram_data histogram data None
(∞:∞)
real
Yes
Examples
eye_jitter=FrontPanel_pp_rms_jitter(histogram_data)
peak2peak_jitter=eye_jitter[0]
rms_jitter=eye_jitter[1]
130
Measurement Expressions
Defined in
$HPEESOF_DIR/expressions/ael/FrontPanel_fun.ael
See Also
eye_binning() (expmeas), eye_density() (expmeas), FrontPanel_eye() (expmeas),
FrontPanel_eye_2d_indepvar_maximum_inner() (expmeas),
FrontPanel_eye_amplitude_histogram() (expmeas), FrontPanel_eye_crossings()
(expmeas), FrontPanel_eye_delay() (expmeas), FrontPanel_eye_fall_trace() (expmeas),
FrontPanel_eye_horizontal_histogram() (expmeas), FrontPanel_eye_regular() (expmeas),
FrontPanel_eye_rise_trace() (expmeas), FrontPanel_eye_risefall_marker() (expmeas),
FrontPanel_eye_topbase() (expmeas), FrontPanel_get_histogram_mean_stddev()
(expmeas), FrontPanel_wave_1st_falling_edge_period() (expmeas),
FrontPanel_wave_1st_rising_edge_period() (expmeas),
FrontPanel_wave_1st_transition_fall_time() (expmeas),
FrontPanel_wave_1st_transition_rise_time() (expmeas), FrontPanel_wave_datarate()
(expmeas), FrontPanel_wave_negative_pulse_width() (expmeas),
FrontPanel_wave_positive_pulse_width() (expmeas), FrontPanel_wave_topbase()
(expmeas)
Notes/Equations
The FrontPanel_pp_rms_jitter() function essentially takes histogram data, and returns
peak to peak jitter by determining non-zero start and stop values and one standard
deviation. The first element of the array represents peak-to-peak value and the second
element represents one standard deviation.
FrontPanel_wave_1st_falling_edge_period()
Given time domain voltage waveform, the logic levels, and the threshold levels, returns
first falling edge period
Syntax
y=
FrontPanel_wave_1st_falling_edge_period(data,base,top,base_threshold_pct,top_threshold_pct)
Arguments
Name
Description
Default Range Type Required
data
time domain voltage waveform None
(∞:∞)
real
Yes
base
logic level zero voltage level
None
(∞:∞)
real
Yes
top
logic level one voltage level
None
(∞:∞)
real
Yes
base_threshold_pct low threshold point
None
(∞:∞)
real
Yes
high_threshold_pct high threshold point
None
(∞:∞)
real
Yes
131
Measurement Expressions
Examples
get_rise_time=FrontPanel_wave_1st_falling_edge_period(data,-1.0,1.0,20,80)
Defined in
$HPEESOF_DIR/expressions/ael/FrontPanel_fun.ael
See Also
eye_binning() (expmeas), eye_density() (expmeas), FrontPanel_eye() (expmeas),
FrontPanel_eye_2d_indepvar_maximum_inner() (expmeas),
FrontPanel_eye_amplitude_histogram() (expmeas), FrontPanel_eye_crossings()
(expmeas), FrontPanel_eye_delay() (expmeas), FrontPanel_eye_fall_trace() (expmeas),
FrontPanel_eye_horizontal_histogram() (expmeas), FrontPanel_eye_regular() (expmeas),
FrontPanel_eye_rise_trace() (expmeas), FrontPanel_eye_risefall_marker() (expmeas),
FrontPanel_eye_topbase() (expmeas), FrontPanel_get_histogram_mean_stddev()
(expmeas), FrontPanel_pp_rms_jitter() (expmeas),
FrontPanel_wave_1st_rising_edge_period() (expmeas),
FrontPanel_wave_1st_transition_fall_time() (expmeas),
FrontPanel_wave_1st_transition_rise_time() (expmeas), FrontPanel_wave_datarate()
(expmeas), FrontPanel_wave_negative_pulse_width() (expmeas),
FrontPanel_wave_positive_pulse_width() (expmeas), FrontPanel_wave_topbase()
(expmeas)
Notes/Equations
Period is a measure of the time between the first detected edge of a waveform and the
next occurrence of the same type of edge. The time between the edges of the waveform
used for measurement is taken at the middle threshold crossings. The
FrontPanel_wave_1st_falling_edge_period() function essentially takes time domain data
and returns the first falling edge period.
FrontPanel_wave_1st_rising_edge_period()
Given time domain voltage waveform, the logic levels, and the threshold levels, returns
first rising edge period
Syntax
y=
FrontPanel_wave_1st_rising_edge_period(data,base,top,base_threshold_pct,top_threshold_pct)
Arguments
132
Measurement Expressions
Name
Description
Default Range Type Required
data
time domain voltage waveform None
(∞:∞)
real
Yes
base
logic level zero voltage level
None
(∞:∞)
real
Yes
top
logic level one voltage level
None
(∞:∞)
real
Yes
base_threshold_pct low threshold point
None
(∞:∞)
real
Yes
high_threshold_pct high threshold point
None
(∞:∞)
real
Yes
Examples
get_rising_period=FrontPanel_wave_1st_rising_edge_period(data,-1.0,1.0,20,80)
Defined in
$HPEESOF_DIR/expressions/ael/FrontPanel_fun.ael
See Also
eye_binning() (expmeas), eye_density() (expmeas), FrontPanel_eye() (expmeas),
FrontPanel_eye_2d_indepvar_maximum_inner() (expmeas),
FrontPanel_eye_amplitude_histogram() (expmeas), FrontPanel_eye_crossings()
(expmeas), FrontPanel_eye_delay() (expmeas), FrontPanel_eye_fall_trace() (expmeas),
FrontPanel_eye_horizontal_histogram() (expmeas), FrontPanel_eye_regular() (expmeas),
FrontPanel_eye_rise_trace() (expmeas), FrontPanel_eye_risefall_marker() (expmeas),
FrontPanel_eye_topbase() (expmeas), FrontPanel_get_histogram_mean_stddev()
(expmeas), FrontPanel_pp_rms_jitter() (expmeas),
FrontPanel_wave_1st_falling_edge_period() (expmeas),
FrontPanel_wave_1st_transition_fall_time() (expmeas),
FrontPanel_wave_1st_transition_rise_time() (expmeas), FrontPanel_wave_datarate()
(expmeas), FrontPanel_wave_negative_pulse_width() (expmeas),
FrontPanel_wave_positive_pulse_width() (expmeas), FrontPanel_wave_topbase()
(expmeas)
Notes/Equations
Period is a measure of the time between the first detected edge of a waveform and the
next occurrence of the same type of edge. The time between the edges of the waveform
used for measurement is taken at the middle threshold crossings. The
FrontPanel_wave_1st_rising_edge_period() function essentially takes time domain data
and returns the first rising edge period.
FrontPanel_wave_1st_transition_fall_time()
Given time domain voltage waveform, the logic levels, and the threshold levels, returns
wave first negative transition fall time
133
Measurement Expressions
Syntax
y=
FrontPanel_wave_1st_transition_fall_time(data,base,top,base_threshold_pct,top_threshold_pct)
Arguments
Name
Description
Default Range Type Required
data
time domain voltage waveform None
(∞:∞)
real
Yes
base
logic level zero voltage level
None
(∞:∞)
real
Yes
top
logic level one voltage level
None
(∞:∞)
real
Yes
base_threshold_pct low threshold point
None
(∞:∞)
real
Yes
high_threshold_pct high threshold point
None
(∞:∞)
real
Yes
Examples
get_rise_time=FrontPanel_wave_1st_transition_fall_time(data,-1.0,1.0,20,80)
Defined in
$HPEESOF_DIR/expressions/ael/FrontPanel_fun.ael
See Also
eye_binning() (expmeas), eye_density() (expmeas), FrontPanel_eye() (expmeas),
FrontPanel_eye_2d_indepvar_maximum_inner() (expmeas),
FrontPanel_eye_amplitude_histogram() (expmeas), FrontPanel_eye_crossings()
(expmeas), FrontPanel_eye_delay() (expmeas), FrontPanel_eye_fall_trace() (expmeas),
FrontPanel_eye_horizontal_histogram() (expmeas), FrontPanel_eye_regular() (expmeas),
FrontPanel_eye_rise_trace() (expmeas), FrontPanel_eye_risefall_marker() (expmeas),
FrontPanel_eye_topbase() (expmeas), FrontPanel_get_histogram_mean_stddev()
(expmeas), FrontPanel_pp_rms_jitter() (expmeas),
FrontPanel_wave_1st_falling_edge_period() (expmeas),
FrontPanel_wave_1st_rising_edge_period() (expmeas),
FrontPanel_wave_1st_transition_rise_time() (expmeas), FrontPanel_wave_datarate()
(expmeas), FrontPanel_wave_negative_pulse_width() (expmeas),
FrontPanel_wave_positive_pulse_width() (expmeas), FrontPanel_wave_topbase()
(expmeas)
Notes/Equations
The FrontPanel_wave_1st_transition_rise_time() function essentially takes time domain
data and measures the fall time of the first negative edge of the waveform. The fall time
will not be measured until the falling edge completes the transition through the upper and
lower threshold.
134
Measurement Expressions
FrontPanel_wave_1st_transition_rise_time()
Given time domain voltage waveform, the logic levels, and the threshold levels, returns
wave first transition rise time
Syntax
y=
FrontPanel_wave_1st_transition_rise_time(data,base,top,base_threshold_pct,top_threshold_pct)
Arguments
Name
Description
Default Range Type Required
data
time domain voltage waveform None
(∞:∞)
real
Yes
base
logic level zero voltage level
None
(∞:∞)
real
Yes
top
logic level one voltage level
None
(∞:∞)
real
Yes
base_threshold_pct low threshold point
None
(∞:∞)
real
Yes
high_threshold_pct high threshold point
None
(∞:∞)
real
Yes
Examples
get_rise_time=FrontPanel_wave_1st_transition_rise_time(data,-1.0,1.0,20,80)
Defined in
$HPEESOF_DIR/expressions/ael/FrontPanel_fun.ael
See Also
eye_binning() (expmeas), eye_density() (expmeas), FrontPanel_eye() (expmeas),
FrontPanel_eye_2d_indepvar_maximum_inner() (expmeas),
FrontPanel_eye_amplitude_histogram() (expmeas), FrontPanel_eye_crossings()
(expmeas), FrontPanel_eye_delay() (expmeas), FrontPanel_eye_fall_trace() (expmeas),
FrontPanel_eye_horizontal_histogram() (expmeas), FrontPanel_eye_regular() (expmeas),
FrontPanel_eye_rise_trace() (expmeas), FrontPanel_eye_risefall_marker() (expmeas),
FrontPanel_eye_topbase() (expmeas), FrontPanel_get_histogram_mean_stddev()
(expmeas), FrontPanel_pp_rms_jitter() (expmeas),
FrontPanel_wave_1st_falling_edge_period() (expmeas),
FrontPanel_wave_1st_rising_edge_period() (expmeas),
FrontPanel_wave_1st_transition_fall_time() (expmeas), FrontPanel_wave_datarate()
(expmeas), FrontPanel_wave_negative_pulse_width() (expmeas),
FrontPanel_wave_positive_pulse_width() (expmeas), FrontPanel_wave_topbase()
(expmeas)
135
Measurement Expressions
Notes/Equations
The FrontPanel_wave_1st_transition_rise_time() function essentially takes time domain
data and measures the rise time of the first positive edge of the waveform. The rise time
will not be measured until the rising edge completes the transition through the lower and
upper threshold.
FrontPanel_wave_datarate()
Estimate data rate from NRZ bitstream
Syntax
y = FrontPanel_wave_datarate(Vout_time,Data_Type)
Arguments
Name
Description
Default Range Type Required
Vout_time time domain voltage waveform None
(∞:∞)
Real Yes
Examples
Find_datarate = FrontPanel_wave_datarate(vout,"NRZ")
Defined in
$HPEESOF_DIR/expressions/ael/FrontPanel_fun.ael
See Also
eye_binning() (expmeas), eye_density() (expmeas), FrontPanel_eye() (expmeas),
FrontPanel_eye_2d_indepvar_maximum_inner() (expmeas),
FrontPanel_eye_amplitude_histogram() (expmeas), FrontPanel_eye_crossings()
(expmeas), FrontPanel_eye_delay() (expmeas), FrontPanel_eye_fall_trace() (expmeas),
FrontPanel_eye_horizontal_histogram() (expmeas), FrontPanel_eye_regular() (expmeas),
FrontPanel_eye_rise_trace() (expmeas), FrontPanel_eye_risefall_marker() (expmeas),
FrontPanel_eye_topbase() (expmeas), FrontPanel_get_histogram_mean_stddev()
(expmeas), FrontPanel_pp_rms_jitter() (expmeas),
FrontPanel_wave_1st_falling_edge_period() (expmeas),
FrontPanel_wave_1st_rising_edge_period() (expmeas),
FrontPanel_wave_1st_transition_fall_time() (expmeas),
FrontPanel_wave_1st_transition_rise_time() (expmeas),
FrontPanel_wave_negative_pulse_width() (expmeas),
FrontPanel_wave_positive_pulse_width() (expmeas), FrontPanel_wave_topbase()
(expmeas)
Notes/Equations
The FrontPanel_wave_datarate() estimate the data rate of the NRZ bit stream.
FrontPanel_wave_negative_pulse_width()
136
Measurement Expressions
Given time domain voltage waveform, the logic levels, and the threshold levels, returns
negative pulse width of the first cycle
Syntax
y=
FrontPanel_wave_negative_pulse_width(data,base,top,base_threshold_pct,top_threshold_pct)
Arguments
Name
Description
data
time domain voltage waveform None
Default Range Type Required
(∞:∞)
real
Yes
base
logic level zero voltage level
None
(∞:∞)
real
Yes
top
logic level one voltage level
None
(∞:∞)
real
Yes
base_threshold_pct low threshold point
None
(∞:∞)
real
Yes
high_threshold_pct high threshold point
None
(∞:∞)
real
Yes
Examples
get_negative_pulse_width=FrontPanel_wave_negative_pulse_width(data,1.0,1.0,20,80)
Defined in
$HPEESOF_DIR/expressions/ael/FrontPanel_fun.ael
See Also
eye_binning() (expmeas), eye_density() (expmeas), FrontPanel_eye() (expmeas),
FrontPanel_eye_2d_indepvar_maximum_inner() (expmeas),
FrontPanel_eye_amplitude_histogram() (expmeas), FrontPanel_eye_crossings()
(expmeas), FrontPanel_eye_delay() (expmeas), FrontPanel_eye_fall_trace() (expmeas),
FrontPanel_eye_horizontal_histogram() (expmeas), FrontPanel_eye_regular() (expmeas),
FrontPanel_eye_rise_trace() (expmeas), FrontPanel_eye_risefall_marker() (expmeas),
FrontPanel_eye_topbase() (expmeas), FrontPanel_get_histogram_mean_stddev()
(expmeas), FrontPanel_pp_rms_jitter() (expmeas),
FrontPanel_wave_1st_falling_edge_period() (expmeas),
FrontPanel_wave_1st_rising_edge_period() (expmeas),
FrontPanel_wave_1st_transition_fall_time() (expmeas),
FrontPanel_wave_1st_transition_rise_time() (expmeas), FrontPanel_wave_datarate()
(expmeas), FrontPanel_wave_positive_pulse_width() (expmeas),
FrontPanel_wave_topbase() (expmeas)
Notes/Equations
137
Measurement Expressions
Negative pulse width is defined as the time from the mid-threshold of the first falling edge
to the mid-threshold of the next rising edge. The
FrontPanel_wave_negative_pulse_width() function essentially takes time domain data and
returns the first negative pulse width.
FrontPanel_wave_positive_pulse_width()
Given time domain voltage waveform, the logic levels, and the threshold levels, returns
positive pulse width of the first cycle
Syntax
y=
FrontPanel_wave_positive_pulse_width(data,base,top,base_threshold_pct,top_threshold_pct)
Arguments
Name
Description
data
time domain voltage waveform None
Default Range Type Required
(∞:∞)
real
Yes
base
logic level zero voltage level
None
(∞:∞)
real
Yes
top
logic level one voltage level
None
(∞:∞)
real
Yes
base_threshold_pct low threshold point
None
(∞:∞)
real
Yes
high_threshold_pct high threshold point
None
(∞:∞)
real
Yes
Examples
get_negative_pulse_width=FrontPanel_wave_positive_pulse_width(data,1.0,1.0,20,80)
Defined in
$HPEESOF_DIR/expressions/ael/FrontPanel_fun.ael
See Also
eye_binning() (expmeas), eye_density() (expmeas), FrontPanel_eye() (expmeas),
FrontPanel_eye_2d_indepvar_maximum_inner() (expmeas),
FrontPanel_eye_amplitude_histogram() (expmeas), FrontPanel_eye_crossings()
(expmeas), FrontPanel_eye_delay() (expmeas), FrontPanel_eye_fall_trace() (expmeas),
FrontPanel_eye_horizontal_histogram() (expmeas), FrontPanel_eye_regular() (expmeas),
FrontPanel_eye_rise_trace() (expmeas), FrontPanel_eye_risefall_marker() (expmeas),
FrontPanel_eye_topbase() (expmeas), FrontPanel_get_histogram_mean_stddev()
(expmeas), FrontPanel_pp_rms_jitter() (expmeas),
FrontPanel_wave_1st_falling_edge_period() (expmeas),
FrontPanel_wave_1st_rising_edge_period() (expmeas),
FrontPanel_wave_1st_transition_fall_time() (expmeas),
FrontPanel_wave_1st_transition_rise_time() (expmeas), FrontPanel_wave_datarate()
138
Measurement Expressions
(expmeas), FrontPanel_wave_negative_pulse_width() (expmeas),
FrontPanel_wave_topbase() (expmeas)
Notes/Equations
Positive pulse width is defined as the time from the mid-threshold of the first rising edge
to the mid-threshold of the next falling edge. The
FrontPanel_wave_positive_pulse_width() function essentially takes time domain data and
returns the first positive pulse width.
FrontPanel_wave_topbase()
Given amplitude histogram of a time domain waveform, returns logic level one and zero
statistics
Syntax
y = FrontPanel_wave_topbase(data,data_type)
Arguments
Name
Description
Default Range Type Required
data
amplitude histogram data
None
(∞:∞)
real
Yes
None
(∞:∞)
real
Yes
data_type data type, only "NRZ" data is supported in current
release
Examples
get_level=FrontPanel_wave_topbase(amplitude_histogram,"NRZ")
top_data=get_level[0::3]
level_one_mean=top_data[0]
level_one_stddev=top_data[1]
level_one_start=top_data[2]
level_one_stop=top_data[3]
base_data=get_level[4::7]
level_zero_mean=base_data[0]
level_zero_stddev=base_data[1]
level_zero_start=base_data[2]
level_zero_stop=base_data[3]
Defined in
$HPEESOF_DIR/expressions/ael/FrontPanel_fun.ael
See Also
eye_binning() (expmeas), eye_density() (expmeas), FrontPanel_eye() (expmeas),
FrontPanel_eye_2d_indepvar_maximum_inner() (expmeas),
FrontPanel_eye_amplitude_histogram() (expmeas), FrontPanel_eye_crossings()
(expmeas), FrontPanel_eye_delay() (expmeas), FrontPanel_eye_fall_trace() (expmeas),
139
Measurement Expressions
FrontPanel_eye_horizontal_histogram() (expmeas), FrontPanel_eye_regular() (expmeas),
FrontPanel_eye_rise_trace() (expmeas), FrontPanel_eye_risefall_marker() (expmeas),
FrontPanel_eye_topbase() (expmeas), FrontPanel_get_histogram_mean_stddev()
(expmeas), FrontPanel_pp_rms_jitter() (expmeas),
FrontPanel_wave_1st_falling_edge_period() (expmeas),
FrontPanel_wave_1st_rising_edge_period() (expmeas),
FrontPanel_wave_1st_transition_fall_time() (expmeas),
FrontPanel_wave_1st_transition_rise_time() (expmeas), FrontPanel_wave_datarate()
(expmeas), FrontPanel_wave_negative_pulse_width() (expmeas),
FrontPanel_wave_positive_pulse_width() (expmeas)
Notes/Equations
The FrontPanel_wave_topbase() function essentially takes amplitude histogram data and
returns logic level one and zero statistics as an array.
140
Measurement Expressions
FrontPanel S-Parameter TDR Functions
This section describes the S-Parameter TDR FrontPanel and associated functions in detail.
The majority of these functions are not generalized functions; they are provided
specifically to support the S-Parameter TDR FrontPanel utility available from the Data
Display. Any function with the prefix "FrontPanel_TDR" requires a special data structure
for input parameters.
FrontPanel_TDRExtrapolate() (expmeas)
FrontPanel_TDREye() (expmeas)
FrontPanel_TDRFreqMode() (expmeas)
FrontPanel_TDRFreqScale() (expmeas)
FrontPanel_TDRFreqSweep() (expmeas)
FrontPanel_TDRGate() (expmeas)
FrontPanel_TDRIFW() (expmeas)
FrontPanel_TDRInversePeeling() (expmeas)
FrontPanel_TDRPeeling() (expmeas)
FrontPanel_TDRPortExt() (expmeas)
FrontPanel_TDRPortMap() (expmeas)
FrontPanel_TDRSmooth() (expmeas)
FrontPanel_TDRTimeScale() (expmeas)
FrontPanel_TDRTimeSweep() (expmeas)
FrontPanel_TDRWindow() (expmeas)
tdr_inverse_peeling() (expmeas)
tdr_peeling() (expmeas)
Note
Any function with the prefix "FrontPanel_TDR" requires a special data structure for input parameters and
is used exclusively by the S-Parameter TDR FrontPanel.
FrontPanel_TDRExtrapolate()
Extrapolates frequency data with the ability to add a DC and low frequency points
Syntax
y = FrontPanel_TDRExtrapolate(Data, Flag, DCFlag, OptFlag, DCValue, Step, PolyList)
Arguments
Name
Description
Default Range Type
Required
Data
frequency transfer function †
None
(∞:∞)
Complex
Array
Yes
Flag
boolean flag if set FALSE will return the original waveform
None
[0:1]
Real
Yes
DCFlag
boolean flag if set TRUE a DC point will be added before
Extrapolate
None
[0:1]
Real
Yes
OptFlag boolean flag if set TRUE an optimizer is run on extrapolated
data
None
[0:1]
Real
Yes
DCValue array of values at DC (one value for each S parameter)
None
(∞:∞)
Real
Yes
Step
None
(0:∞)
Real
Yes
None
(1:∞)
List
Yes
frequency step after Extrapolate
PolyList list data type representing parameters for extrapolation list(even order, even num points, odd order, odd num
points)
141
Measurement Expressions
† The multi-dimensional S parameter array can be created with FP_TDRFreq1Dto3D(S).
Examples
ExtrapolateOut = FrontPanel_TDRExtrapolate(FP_TDRFreq1Dto3D(S), TRUE, TRUE,
TRUE, [0,1,1,0], 1e9, list(3,5,3,5))
Note
Any function with the prefix "FrontPanel_TDR" requires a special data structure for input parameters and
is used exclusively by the S-Parameter TDR FrontPanel.
FrontPanel_TDREye()
Returns the eye waveform produced by running a randomly generated NRZ trace through
the system described by the input S parameter
Syntax
y = FrontPanel_TDREye(Data, NumBits, DataRate, BitSpan, Vmax)
Arguments
Name
Description
Default Range Type
Required
Data
frequency transfer function †
None
(∞:∞)
Complex
Array
Yes
NumBits number of bits in NRZ waveform
None
[1:∞)
Real
Yes
DataRate data rate of NRZ wafeform
None
[1:∞)
Real
Yes
BitSpan
number of samples per bit of NRZ
waveform
None
[1:∞)
Real
Yes
Vmax
maximum voltage for NRZ waveform
None
(∞:∞)
Real
Yes
Vmin
minimum voltage for NRZ waveform
None
(∞:∞)
Real
Yes
† The multi-dimensional S parameter array can be created with FP_TDRFreq1Dto3D(S).
Examples
EyeOut = FrontPanel_TDREye(S11, 101, 1 GHz, 5, 1)
Note
Any function with the prefix "FrontPanel_TDR" requires a special data structure for input parameters and
is used exclusively by the S-Parameter TDR FrontPanel.
FrontPanel_TDRFreqMode()
Returns single-ended or mixed-mode S parameters for 4-port datasets
Syntax
y = FrontPanel_TDRFreqMode(Data, Mode)
Arguments
142
Measurement Expressions
Name Description
Default Range Type
Required
Data
frequency transfer function † None
(∞:∞)
Complex
Array
Yes
Mode
type of frequency mode † †
[0:4]
Real
Yes
None
† The multi-dimensional S parameter array can be created with FP_TDRFreq1Dto3D(S).
† † The different type of modes are:
Mode = 0 Single-Ended
Mode = 1 Differential
Mode = 2 Common
Mode = 3 Differential-Common
Mode = 4 Common-Differential
Any Mode > 0 is only valid for 4-port S parameters
Examples
FreqModeOut = FrontPanel_TDRFreqMode(FP_TDRFreq1Dto3D(S), 0)
Note
Any function with the prefix "FrontPanel_TDR" requires a special data structure for input parameters and
is used exclusively by the S-Parameter TDR FrontPanel.
FrontPanel_TDRFreqScale()
Scales raw frequency data
Syntax
y = FrontPanel_TDRFreqScale(Data, Scale)
Arguments
Name Description
Default Range Type
Required
Data
frequency transfer function † None
(∞:∞)
Complex
Array
Yes
Scale
type of scaling † †
[0:4]
Real
Yes
None
† The multi-dimensional S parameter array can be created with FP_TDRFreq1Dto3D(S).
† † The available scale types are:
Scale = 0 dB
Scale = 1 Magnitude
Scale = 2 Phase
Scale = 3 Real
Scale = 4 Imaginary
Examples
FreqScaleOut = FrontPanel_TDRFreqScale(FP_TDRFreq1Dto3D(S), 1)
Note
Any function with the prefix "FrontPanel_TDR" requires a special data structure for input parameters and
is used exclusively by the S-Parameter TDR FrontPanel.
FrontPanel_TDRFreqSweep()
Performs the time-to-frequency transform across multiple dimensions
Syntax
143
Measurement Expressions
y = FrontPanel_TDRFreqSweep(Data, Flag, Mode, Start, Stop, NumPoints, FArray)
Arguments
Name
Description
Default Range Type
Required
Data
multi-dimensional time waveform †
None
(∞:∞)
Complex
Array
Yes
Flag
boolean flag if set FALSE default sweep values are used
None
[0:1]
Real
Yes
Mode
type of time mode (0 = Lowpass Impulse, 1 = Lowpass
Step, 2 = Bandpass Impulse, 3 = Bandpass Step)
None
[0:2]
Real
Yes
Start
start frequency
None
[0:∞)
Real
Yes
Stop
stop frequency
None
[0:∞)
Real
Yes
NumPoints number of frequency points
None
[1:∞)
Real
Yes
FArray
None
(∞:∞)
Real Array
Yes
frequency sweep of the initial S parameter waveform
† The input data is a multi-dimensional temporal array representing the time transform of
an S parameter array.
The multi-dimensional S parameter array can be created with FP_TDRFreq1Dto3D(S).
Examples
FreqSweepOut = FrontPanel_TDRFreqSweep(ts(FP_TDRFreq1Dto3D(S)), TRUE, 0, 1 GHz,
101, 0)
Note
Any function with the prefix "FrontPanel_TDR" requires a special data structure for input parameters and
is used exclusively by the S-Parameter TDR FrontPanel.
FrontPanel_TDRGate()
Returns a gated time waveform
Syntax
y = FrontPanel_TDRGate(Data, Flag, Start, Length, OutFlag, ResponseType, sm, sn)
Arguments
Name
Description
Default Range Type
Required
Data
multi-dimensional time waveform †
None
Flag
Start
(∞:∞)
Real
Array
Yes
boolean flag if set FALSE will return the original waveform None
[0,1]
Real
Yes
gate start time for each time waveform
None
(∞:∞)
Real
Array
Yes
Length
gate length time for each time waveform
None
(0:∞)
Real
Array
Yes
OutFlag
boolean flag if set TRUE will zero values inside the gate
None
[0,1]
Real
Yes
None
[0:3]
Real
Yes
ResponseType gate response type: (0) standard gate for impulse modes
or (1) flat, (2) linear, or (3) hyperbolic for step modes
† The input data is a multi-dimensional temporal array representing the time transform of
an S parameter array.
The multi-dimensional S parameter array can be created with FP_TDRFreq1Dto3D(S).
Examples
144
Measurement Expressions
GateOut = FrontPanel_TDRGate(ts(FP_TDRFreq1Dto3D(S)), GateMask, TRUE, FALSE)
Note
Any function with the prefix "FrontPanel_TDR" requires a special data structure for input parameters and
is used exclusively by the S-Parameter TDR FrontPanel.
FrontPanel_TDRIFW()
Converts an IFW dataset to S parameters
Syntax
y = FrontPanel_TDRIFW(DatasetName)
Arguments
Name
Description
DatasetName name of IFW
dataset
Default Range Type Required
None
None
String Yes
Examples
IFWOut = FrontPanel_TDRIFW("my_sym.ds")
FrontPanel_TDRInversePeeling()
Note
Any function with the prefix "FrontPanel_TDR" requires a special data structure for input parameters and
is used exclusively by the S-Parameter TDR FrontPanel.
FrontPanel_TDRInversePeeling() is a wrapper function for tdr_inverse_peeling()
(expmeas).
Note
Any function with the prefix "FrontPanel_TDR" requires a special data structure for input parameters and
is used exclusively by the S-Parameter TDR FrontPanel.
FrontPanel_TDRPeeling()
Applies the peeling algorithm to all ports of an S parameter array
Syntax
y = FrontPanel_TDRPeeling(Data, Flag, Step)
Arguments
Name Description
Default Range Type
Required
Data
frequency transfer function †
None
(∞:∞)
Complex
Array
Yes
Flag
boolean flag if set FALSE will return the original waveform None
[0:1]
Real
Yes
Step
voltage step value
(0:∞)
Real
Yes
None
† The multi-dimensional S parameter array can be created with FP_TDRFreq1Dto3D(S).
Examples
PeelingOut = FrontPanel_TDRPeeling(FP_TDRFreq1Dto3D(S), TRUE, 1)
145
Measurement Expressions
Note
Any function with the prefix "FrontPanel_TDR" requires a special data structure for input parameters and
is used exclusively by the S-Parameter TDR FrontPanel.
FrontPanel_TDRPortExt()
Adds a virtual length of ideal transmission line to each port of S parameter data
Syntax
y = FrontPanel_TDRPortExt(Data, Flag, Length, Velocity, LossType, Loss1, Loss2, Freq1,
Freq2)
Arguments
Name
Description
Default Range Type
Required
Data
frequency transfer function †
None
(∞:∞)
Complex
Array
Yes
Flag
boolean flag if set FALSE default sweep values are used
None
[0:1]
Real
Yes
Length
array representing virtual lengths for each port † †
None
(∞:∞)
Real Array
Yes
Velocity
normalized velocity
None
(∞:∞)
Real Array
Yes
LossType array representing loss types for each port (0 = Lossless,
1 = Constant, 2 = Linear) † †
None
(∞:∞)
Real Array
Yes
Loss1
array representing loss in dB for each port (only used for
LossType > 0) † †
None
(∞:∞)
Real Array
Yes
Loss2
array representing loss in dB for each port (only used for
LossType > 1) † †
None
(∞:∞)
Real Array
Yes
Freq1
array representing frequency bin of loss for each port
(only used for LossType > 0) † †
None
(∞:∞)
Real Array
Yes
Freq2
array representing frequency bin of loss for each port
(only used for LossType > 1) † †
None
(∞:∞)
Real Array
Yes
† The multi-dimensional S parameter array can be created with FP_TDRFreq1Dto3D(S).
† † Each parameter for port extensions is the same length as the number of ports in the
input S parameter
Examples
PortExtOut = FrontPanel_TDRPortExt(FP_TDRFreq1Dto3D(S), TRUE, [1,1], [1,1],
[0,0], [3,3], [3,3], [1 Ghz, 1 GHz], [2 GHz, 2 GHz])
Note
Any function with the prefix "FrontPanel_TDR" requires a special data structure for input parameters and
is used exclusively by the S-Parameter TDR FrontPanel.
FrontPanel_TDRPortMap()
Maps input and output ports of an S parameter array
Syntax
y = FrontPanel_TDRPortMap(Data, Flag, MapArray)
Arguments
146
Measurement Expressions
Name
Description
Default Range Type
Required
Data
frequency transfer function †
None
(∞:∞)
Complex
Array
Yes
Flag
boolean flag if set FALSE will return the original waveform None
[0:1]
Real
Yes
[1:∞)
Real
Yes
MapArray array where indicies represent output ports and values
represent input ports
None
† The multi-dimensional S parameter array can be created with FP_TDRFreq1Dto3D(S).
Examples
PortMapOut = FrontPanel_TDRPortMap(FP_TDRFreq1Dto3D(S), TRUE, [1,2,3,4])
Note
Any function with the prefix "FrontPanel_TDR" requires a special data structure for input parameters and
is used exclusively by the S-Parameter TDR FrontPanel.
FrontPanel_TDRSmooth()
Performs the specified smoothing operation on S parameter data
Syntax
y = FrontPanel_TDRSmooth(Data, Flag, Type, ParmList)
Arguments
Name
Description
Default Range Type
Required
Data
frequency transfer function †
None
(∞:∞)
Complex
Array
Yes
Flag
boolean flag if set FALSE will return the original waveform None
[0:1]
Real
Yes
Type
specifies the type of smoothing (0 = moving average, 1 = None
alpha-beta)
[1:∞)
Real
Yes
(0:∞)
Real
Yes
ParmList filter specific parameters (e.g. list(10) for N=10 width
moving average filter)
None
† The multi-dimensional S parameter array can be created with FP_TDRFreq1Dto3D(S).
Examples
SmoothOut = FrontPanel_TDRSmooth(FP_TDRFreq1Dto3D(S), TRUE, 0, list(10))
Note
Any function with the prefix "FrontPanel_TDR" requires a special data structure for input parameters and
is used exclusively by the S-Parameter TDR FrontPanel.
FrontPanel_TDRTimeScale()
Scales raw time data and sweep
Syntax
y = FrontPanel_TDRTimeScale(Data, Scale, Units, Z0, VelocityFactor, TimeModeFlag,
FreqModeFlag, sm, sn)
Arguments
147
Measurement Expressions
Name
Description
Default Range Type
Required
Data
multi-dimensional time waveform †
None
(∞:∞)
Real
Array
Yes
Scale
type of time scale (Scale = 1 for Impedance, Scale = 5
for Ref. Coeff.)
None
[1,5]
Real
Yes
Units
type of sweep units "seconds" or "meters"
None
[0,1]
Real
Yes
Z0
characteristic impedance
50
[1::∞) Real
Yes
VelocityFactor speed of light scale factor
None
[1::∞) Real
Yes
TimeModeFlag time mode flag (see FrontPanel_TDRTimeSweep())
None
[0:1]
Real
Yes
FreqModeFlag freq mode flag (see FrontPanel_TDRFreqMode())
None
[0:1]
Real
Yes
† The input data is a multi-dimensional temporal array representing the time transform of
an S parameter array.
The multi-dimensional S parameter array can be created with FP_TDRFreq1Dto3D(S).
Examples
TimeScaleOut = FrontPanel_TDRTimeScale(ts(FP_TDRFreq1Dto3D(S)), "seconds", 50)
Note
Any function with the prefix "FrontPanel_TDR" requires a special data structure for input parameters and
is used exclusively by the S-Parameter TDR FrontPanel.
FrontPanel_TDRTimeSweep()
Transforms S parameter data into a time waveform
Syntax
y = FrontPanel_TDRTimeSweep(Data, Flag, Mode, Start, Stop, NumPoints)
Arguments
Name
Description
Default Range Type
Required
Data
multi-dimensional frequency transfer function †
None
(∞:∞)
Complex
Array
Yes
Flag
boolean flag if set FALSE default sweep values are used
None
[0:1]
Real
Yes
Mode
type of time mode (0 = Lowpass Impulse, 1 = Lowpass
Step, 2 = Bandpass Impulse, 3 = Bandpass Step)
None
[0:2]
Real
Yes
Start
start time
None
(∞:∞)
Real
Yes
Stop
stop time
None
(∞:∞)
Real
Yes
NumPoints number of time points
None
[1:∞)
Real
Yes
† The multi-dimensional S parameter array can be created with FP_TDRFreq1Dto3D(S).
Examples
TimeSweepOut = FrontPanel_TDRTimeSweep(FP_TDRFreq1Dto3D(S), TRUE, 1, 0, 10 ns,
101)
Note
Any function with the prefix "FrontPanel_TDR" requires a special data structure for input parameters and
is used exclusively by the S-Parameter TDR FrontPanel.
FrontPanel_TDRWindow()
148
Measurement Expressions
Returns windowed S parameter data
Syntax
y = FrontPanel_TDRWindow(Data, Flag, Type, ParmArray)
Arguments
Name
Description
Default Range Type
Required
Data
multi-dimensional frequency transfer function †
None
(∞:∞)
Complex
Array
Yes
Flag
boolean flag if set FALSE will return the original
waveform
None
[0:1]
Real
Yes
Type
specifies the type of window † †
None
[0:6]
Real
Yes
ParmArray list containing window parameter values: list(TimeMode, None
Parm1, Parm2)
None
Real Array
Yes
†
†
0
1
2
3
4
5
The multi-dimensional S parameter array can be created with FP_TDRFreq1Dto3D(S).
† The window types are enumerated by the following:
= Rectangular
= Hanning
= Hamming
= Gaussian
= Kaiser
= Blackman
Examples
WindowOut = FrontPanel_TDRWindow(FP_TDRFreq1Dto3D(S), TRUE, 2, list(0, .42))
tdr_inverse_peeling()
Undoes the layer peeling algorithm on a lossless, peeled, time-domain step response.
Syntax
y = tdr_inverse_peeling(Peeled_Data)
Arguments
Name
Description
Range Type Default Required
Peeled_Data peeled time-domain waveform (-1, 1) real
yes
Examples
y = tdr_inverse_peeling(PeeledResponse)
Defined in
Built in
See Also
tdr_peeling() (expmeas)
Notes/Equations
149
Measurement Expressions
This function is the inverse of the peeling function; thus, excluding numerical sensitivity, y
= tdr_inverse_peeling(tdr_peeling(y)).
tdr_peeling()
Performs TDR peeling or inverse scattering.
Syntax
yTDR = tdr_peeling(TDR_data, TDR_step)
Arguments
Name
Description
Default Range Type Required
TDR_data the TDR data to be impedance
peeled
None
(∞:∞)
Real Yes
TDR_step Step height
0.5
[0:1]
Real No
Examples
peeled=tdr_peeling(vout, 0.5)
Defined in
Built in
See Also
tdr_inverse_peeling() (expmeas)
Notes/Equations
A more detailed explanation of the peeling algorithm can be found in the S-Parameter TDR
FrontPanel (data) documentation.
150
Measurement Expressions
Harmonic Balance Functions For Measurement
Expressions
This section describes the Harmonic Balance functions in detail. The functions are listed in
alphabetical order.
carr to im() (expmeas)
cdrange() (expmeas)
dc to rf() (expmeas)
ifc() (expmeas)
ip3 in() (expmeas)
ip3 out() (expmeas)
ipn() (expmeas)
it() (expmeas)
mix() (expmeas)
pae() (expmeas)
pfc() (expmeas)
phase gain() (expmeas)
pspec() (expmeas)
pt() (expmeas)
remove noise() (expmeas)
sfdr() (expmeas)
snr() (expmeas)
spur track() (expmeas)
spur track with if() (expmeas)
thd func() (expmeas)
ts() (expmeas)
vfc() (expmeas)
vspec() (expmeas)
vt() (expmeas)
Working with Harmonic Balance Data
Harmonic Balance (HB) Analysis produces complex voltages and currents as a function of
frequency or harmonic number. A single analysis produces 1-dimensional data. Individual
harmonic components can be indexed by means of "[ ]". Multi-tone HB also produces 1dimensional data. Individual harmonic components can be indexed as usual by means of
"[ ]". However, the function mix() (expmeas) provides a convenient way to select a
particular mixing component.
carr_to_im()
This measurement gives the suppression (in dB) of a specified IMD product below the
fundamental power at the output port.
Syntax
y = carr_to_im(vOut, fundFreq, imFreq, Mix)
151
Measurement Expressions
Arguments
Name
Description
Default Range Type
Required
vOut
signal voltage at the output port
None
[0:∞)
Real,
Complex
Yes
None
(∞:∞)
Integer
array
Yes
imFreq
harmonic frequency indices for the IMD product of interest None
(∞:∞)
Integer
array
Yes
Mix
consists of all possible vectors of harmonic frequency
(mixing terms) in the analysis †
(∞:∞)
Integer
array
No
fundFreq harmonic frequency indices for the fundamental frequency
None
† It is required whenever the first argument is a spectrum obtained from an expression
that operates on the voltage and/or current spectrums.
Examples
a = carr_to_im(out, {1, 0}, {2, -1})
Defined in
$HPEESOF_DIR/expressions/ael/rf_system_fun.ael
See Also
ip3_out() (expmeas)
cdrange()
Returns compression dynamic range
Syntax
y = cdrange(nf, inpwr_lin, outpwr_lin, outpwr)
Arguments
Name
Description
Default Range Type Required
nf
noise figure at the output port
None
[0:∞)
Real Yes
inpwr_lin
input power in the linear region
None
[0:∞)
Real Yes
None
[0:∞)
Real Yes
output power at 1 dB compression None
[0:∞)
Real Yes
outpwr_lin output power in the linear region
outpwr
Examples
a = cdrange(nf2, inpwr_lin, outpwr_lin, outpwr)
Defined in
$HPEESOF_DIR/expressions/ael/rf_system_fun.ael
152
Measurement Expressions
See Also
sfdr() (expmeas)
Notes/Equations
Used in XDB simulation. The compressive dynamic range ratio identifies the dynamic
range from the noise floor to the 1-dB gain-compression point. The noise floor is the noise
power with respect to the reference bandwidth.
dc_to_rf()
This measurement computes the DC-to-RF efficiency of any part of the network
Syntax
y = dc_to_rf(vPlusRF, vMinusRF, vPlusDC, vMinusDC, currentRF, currentDC,
harm_freq_index, Mix)
Arguments
Name
Description
Default Range Type
Required
vPlusRF
voltage at the positive terminal
None
(∞:∞)
Real,
Complex
Yes
vMinusRF
voltage at the negative terminal
None
(∞:∞)
Real,
Complex
Yes
vPlusDC
DC voltage at the positive terminal
None
(∞:∞)
Real,
Complex
Yes
vMinusDC
DC voltage at the negative terminal
None
(∞:∞)
Real,
Complex
Yes
currentRF
RF current for power calculation
None
(∞:∞)
Real,
Complex
Yes
currentDC
DC current for power calculation
None
(∞:∞)
Real,
Complex
Yes
harm_freq_index harmonic index of the RF frequency at the output
por
None
(∞:∞)
Integer
array
Yes
Mix
None
(∞:∞)
Matrix
No
consists of all possible vectors of harmonic
frequency (mixing terms) in the analysis †
† It is required whenever the first argument is a spectrum obtained from an expression
that operates on the voltage and/or current spectrums.
Examples
a = dc_to_rf(vrf, 0, vDC, 0, I_Probe1.i, SRC1.i, {1,0})
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
ifc()
153
Measurement Expressions
This measurement gives the RMS current value of one frequency-component of a
harmonic balance waveform
Syntax
y = ifc(iOut, harm_freq_index, Mix)
Arguments
Name
Description
Default Range Type
Required
iOut
current through a branch
None
(∞:∞)
Real,
Complex
Yes
harm_freq_index harmonic index of the desired frequency †
None
(∞:∞)
Integer
array
Yes
Mix
None
(∞:∞)
Matrix
No
consists of all possible vectors of harmonic
frequency (mixing terms) in the analysis † †
† Note that the harm_freq_index argument's entry should reflect the number of tones in
the harmonic balance controller. For example, if one tone is used in the controller, there
should be one number inside the braces; two tones would require two numbers separated
by a comma.
† † Mix is required whenever the first argument is a spectrum obtained from an
expression that operates on the voltage and/or current spectrums.
Examples
The following example is for two tones in the harmonic balance controller:
y = ifc(I_Probe1.i, {1, 0})
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
pfc() (expmeas), vfc() (expmeas)
Notes/Equations
This function should not be used for DC measurements. If used, the results will be less by
a factor of sqrt(2.0).
ip3_in()
This measurement determines the input third-order intercept point (in dBm) at the input
port with reference to a system output port.
Syntax
154
Measurement Expressions
y = ip3_in(vOut, ssGain, fundFreq, imFreq, zRef, Mix)
Arguments
Name
Description
Default Range Type
Required
vOut
signal voltage at the output port
None
[0:∞)
Real,
Complex
Yes
ssGain
small signal gain in dB
None
[0:∞)
Real
Yes
fundFreq harmonic frequency indices for the fundamental frequency
None
(∞:∞)
Integer
array
Yes
imFreq
harmonic frequency indices for the intermodulation
frequency
None
(∞:∞)
Integer
array
Yes
zRef
reference impedance
50.0
(∞:∞)
Real,
Complex
No
Mix
consists of all possible vectors of harmonic frequency
(mixing terms) in the analysis †
None
(∞:∞)
Integer
array
No
† It is required whenever the first argument is a spectrum obtained from an expression
that operates on the voltage and/or current spectrums.
Examples
y = ip3_in(vOut, 22, {1, 0}, {2, -1}, 50)
Defined in
$HPEESOF_DIR/expressions/ael/rf_system_fun.ael
See Also
ip3_out() (expmeas), ipn() (expmeas)
Notes/Equations
To measure the third-order intercept point, you must setup a Harmonic Balance simulation
with the input signal driving the circuit in the linear range. Input power is typically set 10
dB below the 1 dB gain compression point. If you simulate the circuit in the nonlinear
region, the calculated results will be incorrect.
ip3_out()
This measurement determines the output third-order intercept point (in dBm) at the
system output port.
Syntax
y = ip3_out(vOut, fundFreq, imFreq, zRef, Mix)
Arguments
155
Measurement Expressions
Name
Description
Default Range Type
Required
vOut
signal voltage at the output port
None
[0:∞)
Real,
Complex
Yes
fundFreq harmonic frequency indices for the fundamental frequency
None
(∞:∞)
Integer
array
Yes
imFreq
harmonic frequency indices for the intermodulation
frequency
None
(∞:∞)
Integer
array
Yes
zRef
reference impedance
50.0
(∞:∞)
Real,
Complex
No
Mix
consists of all possible vectors of harmonic frequency
(mixing terms) in the analysis †
None
(∞:∞)
Integer
array
No
† It is required whenever the first argument is a spectrum obtained from an expression
that operates on the voltage and/or current spectrums.
Examples
y = ip3_out(vOut, {1, 0}, {2, -1}, 50)
Defined in
$HPEESOF_DIR/expressions/ael/rf_system_fun.ael
See Also
ip3_in() (expmeas), ipn() (expmeas)
Notes/Equations
To measure the third-order intercept point, you must setup a Harmonic Balance simulation
with the input signal driving the circuit in the linear range. Input power is typically set 10
dB below the 1 dB gain compression point. If you simulate the circuit in the nonlinear
region, the calculated results will be incorrect.
ipn()
This measurement determines the output nth-order intercept point (in dBm) at the system
output port
Syntax
y = ipn(vPlus, vMinus, iOut, fundFreq, imFreq, n, Mix)
Arguments
156
Measurement Expressions
Name
Description
Default Range Type
Required
vPlus
voltage at the positive output terminal
None
(∞:∞)
Real,
Complex
Yes
vMinus
voltage at the negative output terminal
None
(∞:∞)
Real,
Complex
Yes
iOut
current through a branch
None
(∞:∞)
Real,
Complex
Yes
fundFreq harmonic indices of the fundamental frequency
None
(∞:∞)
Integer
array
Yes
imFreq
harmonic indices of the intermodulation frequency
None
(∞:∞)
Integer
array
Yes
n
order of the intercept
None
[1:∞)
Integer
Yes
Mix
consists of all possible vectors of harmonic frequency
(mixing terms) in the analysis †
None
(∞:∞)
Matrix
No
† It is required whenever the first argument is a spectrum obtained from an expression
that operates on the voltage and/or current spectrums.
Examples
y = ipn(vOut, 0, I_Probe1.i, {1, 0}, {2, -1}, 3)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
ip3_in() (expmeas), ip3_out() (expmeas)
Notes/Equations
To measure the third-order intercept point, you must setup a Harmonic Balance simulation
with the input signal driving the circuit in the linear range. Input power is typically set 10
dB below the 1 dB gain compression point. If you simulate the circuit in the nonlinear
region, the calculated results will be incorrect.
it()
This measurement converts a harmonic-balance current frequency spectrum to a timedomain current waveform.
Syntax
it(iOut, tmin, tmax, numOfPnts)
Arguments
157
Measurement Expressions
Name
Description
Default
Range Type
iOut
current through a
branch
None
(∞:∞)
Real, Complex Yes
tmin
start time
0
[0:∞)
Real
No
tmax
stop time
2*cycle
time
[0:∞)
Real
No
101
[0:∞)
Integer
No
numOfPnts number of points
Required
Examples
y = it(I_Probe1.i, 0, 10nsec, 201)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
vt() (expmeas)
mix()
Returns a component of a spectrum based on a vector of mixing indices
Syntax
mix(xOut, harmIndex, Mix)
Arguments
Name
Description
Default Range Type
Required
xOut
voltage or a current spectrum
None
(∞:∞)
Real,
Complex
Yes
harmIndex desired vector of harmonic frequency indices (mixing
terms)
None
(∞:∞)
Integer
array
Yes
Mix
†
(∞:∞)
Matrix
No †
variable consisting of all possible vectors of harmonic
frequency indices (mixing terms) in the analysis
† Mix, is required whenever the first argument is a spectrum obtained from an expression
that operates on the voltage and/or current spectrums. This is not required if the voltage
is a named node or if the current is from a probe.
Examples
In the example below, vOut is the voltage at a named node. Therefore the third
argument Mix is not required.
y = mix(vOut, {2, -1})
In the example below, vExp is an expression. Therefore in the mix() function,
the third argument Mix is required.
vExp=vOut*vOut/50
z = mix(vExp, {2, -1}, Mix)
Obtain the frequency corresponding to the mixing term {2, -1}
f = mix(freq, {2, -1})
158
Measurement Expressions
In the examples below, Vload is the load voltage from a 2-tone Harmonic Balance
analysis with sweep input power.
f1=mix(freq[0,::],{1,0},Mix[0,::]) returns the fundamental frequency at the
first power point.
freI=vs(freq,freq)
f2=mix(freI,{1,0},Mix) returns the fundamental frequency vs the input power.
Defined in
Built in
See Also
find_index() (expmeas)
Notes/Equations
Used in Harmonic Balance analysis.
It is used to obtain the mixing component of a voltage or a current spectrum
corresponding to particular harmonic frequency indices or mixing terms.
pae()
This measurement computes the power-added efficiency (in percent) of any part of the
circuit
Syntax
y = pae(vPlusOut, vMinusOut, vPlusIn, vMinusIn, vPlusDC, vMinusDC, iOut, iIn, iDC,
outFreq, inFreq)
Arguments
159
Measurement Expressions
Name
Description
Default Range Type
Required
vPlusOut
output voltage at the positive terminal
None
(∞:∞)
Real,
Complex
Yes
vMinusOut output voltage at the negative terminal
None
(∞:∞)
Real,
Complex
Yes
vPlusIn
input voltage at the positive terminal
None
(∞:∞)
Real,
Complex
Yes
vMinusIn
input voltage at the negative terminal
None
(∞:∞)
Real,
Complex
Yes
vPlusDC
DC voltage at the positive terminal
None
(∞:∞)
Real,
Complex
Yes
vMinusDC DC voltage at the negative terminal
None
(∞:∞)
Real,
Complex
Yes
iOut
output current
None
(∞:∞)
Real,
Complex
Yes
iIn
input current
None
(∞:∞)
Real,
Complex
Yes
iDC
DC current
None
(∞:∞)
Real,
Complex
Yes
outFreq
harmonic indices of the fundamental frequency at the
output port
None
(∞:∞)
Integer
array
Yes
inFreq
harmonic indices of the fundamental frequency at the
input port
None
(∞:∞)
Integer
array
Yes
Mix
consists of all possible vectors of harmonic frequency
(mixing terms) in the analysis †
None
(∞:∞)
Matrix
No
† It is required whenever the first argument is a spectrum obtained from an expression
that operates on the voltage and/or current spectrums.
Examples
y = pae(vOut, 0, vIn, 0, v1, 0, I_Probe1.i, I_Probe2.i, I_Probe3.i, 1, 1)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
db() (ael), dbm() (ael)
pfc()
This measurement gives the RMS power value of one frequency component of a harmonic
balance waveform
Syntax
y = pfc(vPlus, vMinus, iOut, harm_freq_index)
Arguments
160
Measurement Expressions
Name
Description
Default Range Type
Required
vPlus
voltage at the positive output terminal
None
(∞:∞)
Real,
Complex
Yes
vMinus
voltage at the negative output terminal
None
(∞:∞)
Real,
Complex
Yes
iOut
current through a branch
None
(∞:∞)
Real,
Complex
Yes
harm_freq_index harmonic index of the desired frequency †
None
(∞:∞)
Integer
array
Yes
Mix
None
(∞:∞)
Matrix
No
consists of all possible vectors of harmonic
frequency (mixing terms) in the analysis † †
† Note that the harm_freq_index argument's entry should reflect the number of tones in
the harmonic balance controller. For example, if one tone is used in the controller, there
should be one number inside the braces; two tones would require two numbers separated
by a comma.
† † Mix is required whenever the first argument is a spectrum obtained from an
expression that operates on the voltage and/or current spectrums.
Examples
y = pfc(vOut, 0, I_Probe1.i, {1, 0})
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
ifc() (expmeas), vfc() (expmeas)
Notes/Equations
This function should not be used for DC measurements. If used, the results will be less by
a factor of 2.0.
phase_gain()
Returns the gain associated with the phase (normally zero)
crossing at associated power. Can be used in Harmonic Balance Analysis of
an oscillator to get the loop-gain. Returns an array of gains.
Syntax
y = phase_gain(Gain, DesiredPhase)
Arguments
161
Measurement Expressions
Name
Description
Default Range Type
Gain
Two dimensional data representing gain. E.g. Loop-gain of None
an oscillator.
DesiredPhase A single value representing the desired phase.
0
Required
(∞:∞)
Complex Yes
(∞:∞)
Real
No
Examples
We assume that a Harmonic Balance analysis has been performed at different
power.
gainAtZeroPhase = phase_gain(Vout/Vin, 0) returns the gain at zero phase.
Defined in
$HPEESOF_DIR/expressions/ael/rf_system_fun.ael
pspec()
This measurement gives a power frequency spectrum in harmonic balance analyses
Syntax
y = pspec(vPlus, vMinus, iOut)
Arguments
Name Description
vPlus
Default Range Type
Required
voltage at the positive node None
(∞:∞)
Real, Complex Yes
vMinus voltage at the negative node None
(∞:∞)
Real, Complex Yes
iOut
(∞:∞)
Real
current through a branch
0
No
Examples
a = pspec(vOut, 0, I_Probe1.i)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
pt() (expmeas), ispec() (expmeas), vspec() (expmeas)
pt()
This measurement calculates the total power of a harmonic balance frequency spectrum.
Syntax
y = pt(vPlus, vMinus, iOut)
162
Measurement Expressions
Arguments
Name Description
vPlus
Default Range Type
Required
voltage at the positive node None
(∞:∞)
Real, Complex Yes
vMinus voltage at the negative node None
(∞:∞)
Real, Complex Yes
iOut
(∞:∞)
Real
current through a branch
0
No
Examples
y = pt(vOut, 0, I_Probe1.i)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
pspec() (expmeas)
remove_noise()
Removes noise floor data from noise data and returns an array.
Syntax
nd = remove_noise(NoiseData, NoiseFloor)
Arguments
Name
Description
Default Range Type
NoiseData Two dimensional array representing noise data
Required
None
(∞:∞)
Real, Complex Yes
NoiseFloor Single dimensional array representing noise floor None
(∞:∞)
Real, Complex Yes
Examples
nd = remove_noise(vnoise, noiseFloor) returns the noise data with the noise
floor removed
Defined in
$HPEESOF_DIR/expressions/ael/rf_system_fun.ael
Notes/Equations
Used in Harmonic Balance analysis.
163
Measurement Expressions
NoiseData is [m,n] where m is receive frequency and n is interference offset frequency. If
NoiseData is [m,n], then NoiseFloor must be [m]. If NoiseData - NosieFloor is less than
zero, then -200 dBm is used.
sfdr()
Returns the spurious-free dynamic range
Syntax
y = sfdr(vOut, ssGain, nf, noiseBW, fundFreq, imFreq, zRef{, Mix})
Arguments
Name
Description
Default Range Type
Required
vOut
signal voltage at the output port
None
[0:∞)
Real,
Complex
Yes
ssGain
small signal gain in dB
None
[0:∞)
Real
Yes
nf
noise figure at the output port
None
[0:∞)
Real
Yes
fundFreq harmonic frequency indices for the fundamental frequency
None
(∞:∞)
Integer
array
Yes
imFreq
harmonic frequency indices for the intermodulation
frequency
None
(∞:∞)
Integer
array
Yes
zRef
reference impedance
50.0
(∞:∞)
Real,
Complex
No
Mix
consists of all possible vectors of harmonic frequency
(mixing terms) in the analysis †
None
(∞:∞)
Integer
array
No
† Mix is required whenever the first argument is a spectrum obtained from an expression
that operates on the voltage and/or current spectrums.
Examples
a = sfdr(vIn, 12, nf2, , {1, 0}, {2, -1}, 50)
Defined in
$HPEESOF_DIR/expressions/ael/rf_system_fun.ael
See Also
ip3_out() (expmeas)
Notes/Equations
Used in a Harmonic Balance and Small-signal S-parameter. It appears in the HB
Simulation palette.
164
Measurement Expressions
This measurement determines the spurious-free dynamic-range ratio for noise power with
respect to the reference bandwidth.
To measure the third-order intercept point, you must setup a Harmonic Balance simulation
with the input signal driving the circuit in the linear range. Input power is typically set 10
dB below the 1 dB gain compression point. If you simulate the circuit in the nonlinear
region, the calculated results will be incorrect.
For the NoiseBW argument, you normally have to use the default value of 1 Hz. If you
increase it, as per the bandwidth of a filter you are using, dynamic range can be greatly
reduced by the resulting rise in the noise floor.
snr()
This measurement gives the ratio of the output signal power (at the fundamental
frequency for a harmonic balance simulation) to the total noise power (in dB).
Syntax
y = snr(vOut, vOut.noise, fundFreq, Mix)
Arguments
Name
Description
Default Range Type
Required
vOut
signal voltage at the output port
None
[0:∞)
Real,
Complex
Yes
vOut.noise noise voltage at the output port
None
[0:∞)
Real,
Complex
Yes
fundFreq
harmonic frequency indices for the fundamental
frequency †
None
(∞:∞)
Integer
array
Yes
Mix
consists of all possible vectors of harmonic frequency
(mixing terms) in the analysis † †
None
(∞:∞)
Integer
array
No
† Note that fundFreq is not optional; it is required for harmonic balance simulations, but it
is not applicable in AC simulations.
† † Mix is required whenever the first argument is a spectrum obtained from an
expression that operates on the voltage and/or current spectrums.
Examples
a = snr(vOut, vOut.noise, {1, 0})
returns the signal-to-power noise ratio for a harmonic balance simulation.
a = snr(vOut, vOut.noise)
returns the signal-to-power noise ratio for an AC simulation.
Defined in
$HPEESOF_DIR/expressions/ael/rf_system_fun.ael
See Also
ns_pwr_int() (expmeas), ns_pwr_ref_bw() (expmeas)
165
Measurement Expressions
Notes/Equations
If the second argument is of higher dimension than the first, the noise bandwidth used for
the purpose of computing snr will be equal to the frequency spacing of the innermost
dimension of the noise data, instead of the standard value of 1 Hz.
spur_track()
Returns the maximum power of all signals appearing in a user-specifiable IF band, as a
single RF input signal is stepped. If there is no IF signal appearing in the specified band,
for a particular RF input frequency, then the function returns an IF signal power of -500
dBm.
Syntax
IFspur = spur_track(vs(vout, freq), if_low, if_high, rout)
Arguments
Name Description
Default Range Type Required
vout
None
None
String Yes
if_low lowest frequency in the IF band
None
[0:∞)
Real
Yes
if_high highest frequency in the IF band
None
[0:∞)
Real
Yes
rout
None
[0:∞)
Real
Yes
IF output node name
load resistance connected to the IF port, necessary for computing
power delivered to the load
Examples
IFspur = spur_track(vs(HB.VIF1, freq), Fiflow[0, 0], Fifhigh[0, 0], 50)
where
VIF1 is the named node at the IF output.
Fiflow is the lowest frequency in the IF band.
Fifhigh is the highest frequency in the IF band.
50 is the IF load resistance.
Fiflow and Fifhigh are passed parameters from the schematic page (although they
can be defined on the data display page instead.) These parameters, although
single-valued on the schematic, become matrices when passed to the dataset,
where each element of the matrix has the same value. The [0, 0] syntax just
selects one element from the matrix.
Defined in
$HPEESOF_DIR/expressions/ael/digital_wireless_fun.ael
See Also
spur_track_with_if() (expmeas)
166
Measurement Expressions
Notes/Equations
Used in Receiver spurious response simulations.
IFspur computed above will be the power in dBm of the maximum signal appearing in the
IF band, versus RF input frequency. Note that it would be easy to modify the function to
compute dBV instead of dBm.
This function is meant to aid in testing the response of a receiver to RF signals at various
frequencies. This function shows the maximum power of all signals appearing in a userspecifiable IF band, as a single RF input signal is stepped. There could be fixed, interfering
tones present at the RF input also, if desired. The maximum IF signal power may be
plotted or listed versus the stepped RF input signal frequency. If there is no IF signal
appearing in the specified band, for a particular RF input frequency, then the function
returns an IF signal power of -500 dBm.
spur_track_with_if()
Returns the maximum power of all signals appearing in a user-specifiable IF band, as a
single RF input signal is stepped. In addition, it shows the IF frequencies and power levels
of each signal that appears in the IF band, as well as the corresponding RF signal
frequency.
Syntax
IFspur = spur_track_with_if(vs(vout, freq), if_low, if_high, rout)
Arguments
Name Description
Default Range Type Required
vout
None
None
String Yes
if_low lowest frequency in the IF band
None
[0:∞)
Real
Yes
if_high highest frequency in the IF band
None
[0:∞)
Real
Yes
rout
None
[0:∞)
Real
Yes
IF output node name
load resistance connected to the IF port, necessary for computing
power delivered to the load
Examples
IFspur=spur_track_with_if(vs(HB.VIF1, freq), Fiflow[0, 0], Fifhigh[0, 0], 50)
where
VIF1 is the named node at the IF output.
Fiflow is the lowest frequency in the IF band.
Fifhigh is the highest frequency in the IF band.
50 is the IF load resistance.
Fiflow and Fifhigh are passed parameters from the schematic page (although they
can be defined on the data display page instead.) These parameters, although
single-valued on the schematic, become matrices when passed to the dataset,
where each element of the matrix has the same value. The [0, 0] syntax just
selects one element from the matrix.
Defined in
$HPEESOF_DIR/expressions/ael/digital_wireless_fun.ael
167
Measurement Expressions
See Also
spur_track() (expmeas)
Notes/Equations
Used in Receiver spurious response simulations.
IFspur computed above will be the power in dBm of the maximum signal appearing in the
IF band, versus RF input frequency. Note that it would be easy to modify the function to
compute dBV instead of dBm.
This function is meant to aid in testing the response of a receiver to RF signals at various
frequencies. This function, similar to the spur_track function, shows the maximum power
of all signals appearing in a user-specifiable IF band, as a single RF input signal is
stepped. In addition, it shows the IF frequencies and power levels of each signal that
appears in the IF band, as well as the corresponding RF signal frequency. There could be
fixed, interfering tones present at the RF input also, if desired. The maximum IF signal
power may be plotted or listed versus the stepped RF input signal frequency.
thd_func()
This measurement returns the Total Harmonic Distortion percentage.
Syntax
y = thd_func(v)
Arguments
Name Description Default Range Type
v
voltage
None
(∞:∞)
Required
Real, Complex Yes
Examples
y = thd_func(Vload)
Defined In
$HPEESOF_DIR/expressions/ael/rf_system_fun.ael
ts()
Performs a frequency-to-time transform
Syntax
y= ts(x, tstart, tstop, numtpts, dim, windowType, windowConst, nptsspec)
Arguments
168
Measurement Expressions
Name
Description
Default
Range
Type
Required
x
frequency-domain data to be
transformed
None
(-∞:∞)
Real
Yes
tstart
starting time
0
[0:∞)
Integer,
Real
No
tstop
stoping time
tstop = tstart +
2.0/fabs(freq[0])
[0:∞)
Integer,
Real
No
numtpts
number of time points
101
[1:∞)
Integer
No
dim
dimension to be transformed
(not used currently)
highest dimension
[1:∞)
Integer
No
windowType type of window to be applied to 0
the data
[0:9] †
Integer,
string
No
windowConst window constant ††
[0:∞)
Integer,
Real
No
nptsspec
0
number of first harmonics to be 1
transformed
[1:NumFreqs] Integer
No
† The window types and their default constants are:
0 = None
1 = Hamming 0.54
2 = Hanning 0.50
3 = Gaussian 0.75
4 = Kaiser 7.865
5 = 8510 6.0 (This is equivalent to the time-to-frequency transformation with normal gate
shape setting in the 8510 series network analyzer.)
6 = Blackman
7 = Blackman-Harris
8 = 8510-Minimum 0
9 = 8510-Maximum 13
†† windowConst is not used if windowType is 8510
Examples
The following examples of ts assume that a harmonic balance simulation was
performed with a fundamental frequency of 1 GHz and order = 8:
Y=ts(vOut) returns the time series (0, 20ps, ... , 2ns)
Y=ts(vOut, 0, 1ns) returns the time series (0, 10ps, ..., 1ns)
Y=ts(vOut, 0, 10ns, 201) returns the time series (0, 50ps, ... , 10ns)
Y=ts(vOut, , , , , , , 3) returns the time series (0, 20ps, ... , 2ns), but
only uses harmonics from 1 to 3 GHz
Defined in
Built in
See Also
fft() (expmeas), fs() (expmeas), fspot() (expmeas)
169
Measurement Expressions
Notes/Equations
Used in Harmonic Balance and Circuit Envelope simulations.
The default number of time points is computed as follows:
if the number of frequencies is < 2, it is set to 101
else use the following formula
newdefault_numtpts =
if the new value
it is set
if it is greater
it is set
fabs(16.0 * 2.0 * freq[ numfreqs-1] / freq[1]);
is less than 101
to 101
than 10001,
to 10001.
So the new default is a value between 101 and 10001, and varies based on the number of
frequencies, and the actual frequency values.
The dim argument is not used and should be left empty in the expression. Entering a
value will have no impact on the results.
ts(x) returns the time domain waveform from a frequency spectrum. When x is a
multidimensional vector, the transform is evaluated for each vector in the specified
dimension. For example, if x is a matrix, then ts(x) applies the transform to every row of
the matrix. If x is three dimensional, then ts(x) is applied in the lowest dimension over the
remaining two dimensions. The dimension over which to apply the transform may be
specified by dimension; the default is the lowest dimension (dimension=1). ts() originated
in MDS and is similar to vt().
Note
Where x is multi-dimensional, the ts (x) function expects frequency to be the most frequently-changing
variable in the input data, and the function may produce unpredictable results if this is not the case. For a
dataset which does not have frequency as the most frequently-changing variable, the problem can be
eliminated by using the permute (x) function to change the dimension order, as follows:
permx = permute(x)
ts(permx)
x must be numeric. It will typically be data from a Harmonic Balance analysis.
By default, two cycles of the waveform are produced with 101 points, starting at time
zero, based on the lowest frequency in the input spectrum. These may be changed by
setting tstart, tstop, or numtpts.
All of the harmonics in the spectrum will be used to generate the time domain waveform.
When the higher-order harmonics are known not to contribute significantly to the time
domain waveform, only the first n harmonics may be requested for the transform, by
setting nptsspec = n.
ts(x) can be used to process more than Harmonic Balance. For example, ts(x) can be used
to convert AC simulation data to a time domain waveform using only one frequency point
in the AC simulation.
Note that if the data does not have an explicit independent variable "freq", it is assumed
to be starting at 0.0 and incremented in steps of 1. In some cases, this might lead to an
170
Measurement Expressions
incorrect time waveform. For example to obtain the time waveform of the second tone in a
single tone analysis, using ts(Vout[2]) would give incorrect results. In this case use
ts(Vout[2::3],,,,,,,1) to obtain the correct waveform.
In harmonic balance analysis if variables are swept, the dataset saved has an inner most
independent harmindex and a first dependent freq . In the case of argument tstop not
being given the default is calculated using the dependent variable freq . But if the
argument x in the ts() function is arithmetically operated or sub-indexed, the dependent
freq is not maintained and in such cases the ts() function returns incorrect time values.
This can be prevented by first using the ts() function on such data and then obtaining the
necessary data. The example below illustrates this point.
Assume that the harmonic balance analysis has swept variable Pin . In this case the data
has two independents [Pin, harmindex]. If Idd.i and Iout.i are 2 currents then the
expression below:
tsERR = ts(Idd.i - Iout.i)
would return the incorrect time axis values. This can be solved by the expression:
tsWORKS = ts(Idd.i) - ts(Iout.i)
Similarly the expression:
tsERR1 = ts(Idd.i[0,::])
would return the incorrect time axis values. This can be solved by the expressions:
ts_Idd = ts(Idd.i)
ts_Idd_0 = ts_Idd[0,::]
vfc()
This measurement gives the RMS voltage value of one frequency-component of a
harmonic balance waveform
Syntax
y = vfc(vPlus, vMinus, harm_freq_index)
Arguments
Name
Description
Default Range Type
Required
vPlus
voltage at the positive output terminal
None
(∞:∞)
Real,
Complex
Yes
vMinus
voltage at the negative output terminal
None
(∞:∞)
Real,
Complex
Yes
harm_freq_index harmonic index of the desired frequency †
None
(∞:∞)
Integer
array
Yes
Mix
None
(∞:∞)
Matrix
No
consists of all possible vectors of harmonic
frequency (mixing terms) in the analysis † †
† Note that the harm_freq_index argument's entry should reflect the number of tones in
the harmonic balance controller. For example, if one tone is used in the controller, there
should be one number inside the braces; two tones would require two numbers separated
by a comma.
† † Mix is required whenever the first argument is a spectrum obtained from an
expression that operates on the voltage and/or current spectrums.
Examples
a = vfc(vOut, 0, {1, 0})
171
Measurement Expressions
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
ifc() (expmeas), pfc() (expmeas)
Notes/Equations
This function should not be used for DC measurements. If used, the results will be less by
a factor of sqrt(2.0).
vspec()
Returns the voltage frequency spectrum
Syntax
y = vspec(vPlus, vMinus)
Arguments
Name Description
vPlus
Default Range Type
Required
voltage at the positive node None
(∞:∞)
Real, Complex Yes
vMinus voltage at the negative node None
(∞:∞)
Real, Complex Yes
Examples
a = vspec(v1, v2)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
ispec() (expmeas), pspec() (expmeas)
Notes/Equations
Used in Harmonic Balance analysis.
This measurement gives a voltage frequency spectrum across any two nodes. The
measurement gives a set of RMS voltages at each frequency.
172
Measurement Expressions
vt()
This measurement converts a harmonic-balance voltage frequency spectrum to a timedomain voltage waveform.
Syntax
y = vt(vPlus, vMinus, tmin, tmax, numOfPnts)
Arguments
Name
Description
vPlus
voltage at the positive node None
(∞:∞)
Real, Complex Yes
vMinus
voltage at the negative node None
(∞:∞)
Real, Complex Yes
tmin
start time
0
[0:∞)
Real
No
tmax
stop time
2*cycle
time
[0:∞)
Real
No
101
[0:∞)
Integer
No
numOfPnts number of points
Default
Range Type
Required
Examples
a = vt(vOut, 0, 0, 10nsec, 201)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
it() (expmeas), ts() (expmeas)
Notes/Equations
The vt() function originated in Series IV and simply calls the frequency to time domain
transformer function, ts(). In some cases, if default values are used for tmin, tmax, and
numOfPnts, the proper results may not be obtained due to an insufficient number of
points. In such cases, the appropriate values for tmin, tmax, and numOfPnts need to be
used. This function uses default values for window type and window constant, and in
certain cases the correct results may not be obtained due to this fact. In this situation,
use the ts() function instead with the proper windowing. For more information, refer to the
Notes/Equations section for the ts() function.
173
Measurement Expressions
Jitter Analysis Functions
This section describes the jitter analysis concepts and functions in detail. These are not
generalized functions, they are provided specifically to support jitter analysis.
bathtub() (expmeas)
jitter separation() (expmeas)
Working with Jitter Analysis Data
Jitter Analysis is used to decompose aggregate total jitter of serial data into the individual
jitter components, random jitter (RJ), and deterministic jitter (DJ) as shown in Jitter
Components. Jitter analysis leverages the techniques from the DCA-J, equivalent-time
sampling, and the Infiniium DSO80000 real-time oscilloscopes.
Jitter Components
Definitions
174
Measurement Expressions
BER
Bit Error Rate
DCD
Duty Cycle Distortion. Derived from the Composite DDJ Histogram graph. It is the absolute
value of the difference between the mean of the histogram of the rising edge positions and the
mean of the histogram of the falling edge positions.
DDJ
Data Dependent Jitter. DDJ is the difference in the position of the earliest edge (rising or falling)
and the latest (rising or falling) edge. If DCD = zero, DDJ = ISI. If ISI = zero, DDJ = DCD.
DDJpp
Data dependent jitter, peak-to-peak value of the jitter that is correlated to the data pattern. It is
the difference in the position of the earliest edge (rising or falling) and the latest (rising or
falling) edge. If DCD=0, DDJ is just ISI. If ISI=0, then DDJ is just DCD.
DJ
Deterministic Jitter. DJ is bounded by a finite magnitude. It can be broken into jitter which is
correlated to the data sequence and jitter that occurs independent of data.
DJ( δδ )
Delta-Delta Deterministic Jitter of the bimodal equivalent model used to represent all aggregate
deterministic jitter as defined in the dual-Dirac model for total jitter. Deterministic jitter is
defined by the dual-Dirac jitter model as all those components of total jitter that do not fit a
Gaussian probability density function. It is given by the time delay separation of the two delta
functions.
ISIpp
Inter-Symbol Interference peak-to-peak (p-p) range of the jitter that is correlated to rising
edges or the jitter that is correlated to falling edges (whichever is greater). ISI is the largest of
the difference between the earliest falling/rising and latest falling/rising edges, determined from
measuring the average position of each bit in the pattern. When doing a jitter analysis if the
rising or falling edge modes are selected, then only the specified edges are used in the
calculation of ISIpp.
MinSeqDDJ Minimum number of sequences needed for a successful DDJ separation.
MinNTIEs
Minimum number of TIEs that are needed if the corresponding number of Nbps is used.
MinNSeqs
Minimum number of sequences that can be used for given NTIEs.
MaxNSeqs Maximum number of sequences that can be used for given MinSeqsDDJ.
Nbps
Number of bits per sequence
Nbpp
Number of bits per pattern
NTIEs
Number of TIEs
NumSeqs
Number of sequences
Nwpps
Number of whole patterns per sequence
PJ
Periodic Jitter. PJ represents all of the periodic jitter that is uncorrelated from the data pattern.
There are 2 types:
PJ( δδ )
Periodic Jitter delta-delta, is the jittered magnitude required to make RJ PDFs match the DualDirac model with the measured or simulated RJ and PJ.
PJrms
The root-mean-square value of the uncorrelated periodic jitter.
RJ
Random Jitter. RJ follows a Gaussian distribution and is represented by the rms value of the RJ
distribution, RJrms. RJ is the baseline noise floor of the aliased power spectrum. Peaks (anything
above a particular threshold) are identified and removed.
RJrms
Random Jitter follows a Gaussian distribution. RJ is the baseline noise floor of the aliased power
spectrum. Anything above it is periodic jitter and is removed in calculating RJ.
TJ
Total Jitter. TJ is interpreted as total eye closure at a specified BER (10-12 default). If the
closure threshold is the default and TJ=50ps, the likelihood that and edge will be 25ps late or
25ps early is 1 in a billion.
TJpp
The peak-to-peak value of the total jitter calculated at a specific bit error rate (BER). The BER
level specified as one of the arguments during jitter analysis identifies the specified BER for
which the TJ value was calculated. This TJpp value is calculated as an estimate of the true total
jitter, as defined by the dual-Dirac jitter model.
Jitter Analysis Process
175
Measurement Expressions
This section describes steps involved in jitter analysis.
Time Interval Error
The first step in the jitter analysis/decomposition process is finding the time interval error
(TIE), which is the time difference between the serial data signal relative to a reference
signal (usually a clock signal) as shown in Time Interval Error. TIE is then used in the
jitter decomposition.
Time Interval Error
Sub-Sampled Decimation for DDJ Separation
After the TIE data has been calculated, the next step is DDJ separation. Jitter analysis can
be done on periodic or arbitrary data. Currently, only periodic data is supported. In order
to decompose jitter, the TIE calculated is associated with the specific bit in the source
signal's logical bit sequence. The TIE data is decimated into sub-sampled TIE data, where
the value in the sub-sampled sequence corresponds to a specific bit within the pattern.
The number of original samples skipped during decimation is a function of the RJ
bandwidth. The narrow-band mode maximizes the decimation ratio, and the wide-band
minimizes the decimation. The next step is to perform a FFT on the sub-sampled data. The
first value of each jitter spectrum (DC component) is the DDJ for the particular bit of the
repeating pattern.
RJ PJ Separation
Once the DDJ component has been subtracted from TJ, the remaining jitter spectrum is
comprised of RJ and PJ. The power spectrum density (PSD) of the RJ/PJ spectrum is
calculated. All of the individual RJ/PJ spectrums are averaged together (as well as
averaged with spectrums from previous sequences) to form the averaged PSD (APSD). All
APSD's frequency components that have a value above a threshold are removed as PJ.
176
Measurement Expressions
The remaining APSD are then combined to obtain RJrms. Refer to Reference 1 in
References for more details.
Viewing Results
Jitter Analysis FrontPanel is part of the Data Display. For information on viewing Jitter
Analysis simulation results, see "Jitter Analysis FrontPanel" in the Data Display
documentation.
BER Bathtub Graph
Bathtub
The BER Bathtub graph plots the sampling time (in UI) of a serial data signal on the X-axis
versus bit error rate on the Y-axis. The trace in red represents BER values that are
calculated directly from the TIE data, and the trace in blue represents BER values that are
extrapolated using the calculated values of RJ and DJ.
The BER value for the TIE data is calculated by integrating the TJ Histogram. The
extrapolated values are obtained from the Dual-Dirac model of the way RJ and DJ combine
into a CDF. RJ is modeled as a Gaussian distribution with standard deviation RJ, and DJ is
modeled as two Dirac-Delta functions, separated by distance DJ. This function is basically
the integral of the function defined by Dual-Dirac PDF model, except that because this is
intended to model BER curves, this CDF has been modified to peak at the transition
density rather than 1.0, for a maximum BER equivalent to the transition density.
The Q of BER bathtub graph plots the sampling time (in UI) versus the Q of BER.
177
Measurement Expressions
Q of BER Bathtub
Jitter Histograms
TJ Histogram
Total Jitter (TJ) Histogram
The Total Jitter (TJ) Histogram shows the combined Random Jitter (RJ), Periodic Jitter (PJ)
and Data Dependent Jitter (DDJ) probability density functions. The TJ histogram is
calculated by cross-correlating the RJ, PJ histogram with the DDJ histogram. It is the a
histogram of all of the measured jitter, both correlated to the data pattern and
uncorrelated to the data pattern, combined in a single histogram. The graph's horizontal
axis indicates negative time for samples that occur earlier than expected and positive time
for samples that occur later than expected.
RJ PJ Histogram
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Measurement Expressions
Random Jitter, Periodic Jitter (RJ, PJ) Histogram
The RJ, PJ Jitter Histogram shows the histogram of all uncorrelated jitter. The graph's
horizontal axis indicates negative time for samples that occur earlier than expected and
positive time for samples that occur later than expected.
Composite TJ Histogram
Composite TJ Histogram
The Composite TJ Histogram shows separate graphs of Total Jitter (TJ), Data-Dependent
Jitter (DDJ), and the combined histogram of uncorrelated Random Jitter (RJ) and
uncorrelated Periodic Jitter (PJ). The graph's horizontal axis indicates negative time for
samples that occur earlier than expected and positive time for samples that occur later
than expected.
Data Dependent Jitter Histogram
179
Measurement Expressions
Data Dependent Jitter (DDJ) Histogram
The Data Dependent Jitter (DDJ) histogram displays the jitter that is correlated to the
data pattern. The graph's horizontal axis indicates negative time for samples that occur
earlier than expected and positive time for samples that occur later than expected. For
data-type source waveform signal, the mean of the histogram of DDJ from all edges is
always equal to zero.
Composite DDJ Histogram
Composite Data Dependent Jitter (DDJ) Histogram
The Composite Data Dependent Jitter (DDJ) Histogram shows three histograms of
correlated jitter based on data from all edges, rising edges, and falling edges. The peakto-peak spread of the all-edges histogram represents the DDJ. The peak-to-peak spread
of the rising-edges histogram or the falling-edges histogram, whichever is greater,
represents Inter-Symbol Interference (ISI). The difference between the mean of the rising
edge positions and the mean of the falling edge positions represents the Duty Cycle
Distortion (DCD). The graph's horizontal axis indicates negative time for samples that
180
Measurement Expressions
occur earlier than expected and positive time for samples that occur later than expected.
DDJ versus Bits Graph
Data Dependent Jitter (DDJ) versus Relative Bit Position
The graph of Data-Dependant Jitter (DDJ) versus Relative Bit Position shows relative bit
position on the horizontal axis. The vertical axis indicates negative time for samples that
occur earlier than expected and positive time for samples that occur later than expected.
The bit numbers displayed on the horizontal axis are relative values only and may change
each time the logical bit pattern of the source waveform is recalculated.
RJ PJ Spectrum
RJ, PJ Spectrum Graph
The RJ, PJ (Random Jitter, Periodic Jitter) Spectrum graph shows the discrete Fourier
transform of the combined RJ and PJ. The vertical axis represents the magnitude of each
181
Measurement Expressions
spectral jitter component and the horizontal axis identifies the frequency. The displayed
magnitude spectrum is calculated independently for each sequenced waveform and then
averaged with magnitude spectrums from previous sequences.
The frequency resolution of the RJ, PJ Spectrum is improved by increasing Nbps, sequence
record length. However, increasing the Nbps can significantly affect calculation time.
Overall calculation time can be improved by not displaying the RJ, PJ Spectrum graph (not
using MeasType equal 4).
References
1. Precision Jitter Analysis Using the Agilent 86100C DCA-J - Agilent Literature Number
5989-1146EN
2. Jitter Analysis: The dual-Dirac Model, RJ/DJ, and Q-Scale - Agilent White Paper 59893206EN
3. MJSQ - Methodologies for Jitter and Signal Quality Specification - T11.2/Project 1316DT
4. Analyzing Jitter Using Agilent EZJIT Plus Software - Application Note 1563
5. Selecting RJ Bandwidth in EZJIT Plus Software - Application Note 1577
6. EZJIT and EZJIT Plus Jitter Analysis Software for Infiniium Serial Oscilloscopes - Data
Sheet 5989-0109EN
7. U nderstanding Jitter and Wander Measurements and Standards - 5988-6254EN
8. Jitter Separation - 50 Mb/s to Over 40 Gb/s Using the Agilent 86100C Infiniium DCAJ, whitepaper, Agilent Technologies, Inc.
http://www.eeplace.com/dm/2802/tw/DCAjwhitepaper3.pdf
bathtub()
This measurement returns the data based and extrapolated bathtub curves and Q curves.
Syntax
BathTub = bathtub(vJitterSig, vRefClkSig, Nbpp, BitPeriod, BERLevel, DataType, Pattern,
Nbps, NumSeq, RJBWMode, EdgeType)
Arguments
182
Measurement Expressions
Name
Description
Default Range
Type
Required
vJitterSig
time-domain based jittered signal
None
(-∞:∞)
Real
Yes
vRefClkSig time-domain based reference clock signal
or bit-period
None
(0:∞)
Real
No
Nbpp
number of bits per pattern
None
2 to 2^17
integer
Yes
BitPeriod
bit period
None
0 < BitPeriod < 1e-3
Real
Yes
BERLevel
BER level at which to measure TJ
1e-12
1e-40 < BERLevel <
1e-1
Real
No
DataType
data-type
1
1 (Periodic),
2(Random) †
Integer
No
Pattern
bit pattern vector or bit pattern file-name
None
0 and 1
Array,
String
No
Nbps
number of bits per sequence
††
[2:Inf]
Integer
No
NumSeq
number of sequences of data to be used in
creating the bathtub
†††
[1:Inf]
Integer
No
RJBWMode RJ Bandwidth Mode
1
1(Narrow), 2(Wide)
Integer
No
EdgeType
3
1(Rising), 2(Falling),
3(Both)
Integer
No
Data Edge Type
Examples
The following example measures the bathtub of a jittered signal that uses a
PRBS10 source:
BathTub = bathtub(vJitSig, vRefClkSig, 1023, 50 ps, 1e-12, 1,, 5000, 95,,)
The returned value BathTub is a list of four measurements - data based BER
curve, extrapolated BER curve, data based Q BER curve and extrapolated Q BER
curve.
DataBath = BathTub[0]
MdlBath = BathTub[1]
DataQBath = BathTub[2]
MdlQBath = BathTub[3]
Where:
vJitterSig is the time-domain jittered signal. The argument jittered signal is the serial
data (time versus amplitude) used in jitter separation. This signal is used in calculating
the zero crossings, and the serial data is calculated from the zero crossings. If there are
no zero crossings, then jitter separation will terminate with an error message. Currently,
only periodic pattern serial data is supported, and the pattern must be repeatable.
Arbitrary or random serial data is not supported.
vRefClkSig can be a reference clock signal (time versus amplitude) or the bit period. If
the clock signal is given, the zero crossings are used to find the clock serial. This zero
crossing is used along with the zero crossings of the jittered data in calculating the Time
Interval Error (TIE). If the bit period is given, then the clock zero crossings are calculated
from the bit period. If not given, the fourth argument bit period is used.
Nbpp is the pattern length and is required in order to automatically detect the pattern. At
minimum this should be 2 (a clock signal) and a maximum of 217 . Note that for larger
pattern length the number of serial bits needed would be large and jitter separation would
take a long time. See Viewing Results (expmeas) for more information.
BitPeriod = Bit period must be greater than 0 and less than 1e-3.
BERLevel is the level at which to calculate TJ, RJpp. This argument is optional and the
default value is 1e-12. For example if the system is being designed for a BER of 1e-12,
then doing a jitter separation at 1e-12 would calculate the TJ at 1e-12.
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Measurement Expressions
Pattern can be an array of 0s and 1s or the name of a file containing the pattern. An
example of a pattern in array format is [1,0,0,0,0,0,0,0,1,0]. A pattern must have a 0 and
a 1. In addition, the minimum pattern is a [0, 1] - a clock signal. If the pattern is given in
a file, the pattern bits must be space separated and in a single line. If pattern is not given,
the pattern is automatically detected from the signal bits. For each sequence of data, the
pattern is detected and compared with the previous sequence patter or the given pattern.
If the pattern matches, that particular sequence of data is used.
Nbps indicates the number of bits-per-acquisition or sequence. Nbps is optional and the
default is 2 * Minimum # Whole Pattern per sequence * Nbpp = 2 * 64 * Nbpp. In most
cases this default value would work, but in some cases this value might need to be set
manually since this argument has a direct bearing on the number of serial bits needed for
a valid jitter separation and the RJPJ separation method. See Viewing Results (expmeas)
for more information.
NumSeqs can be used to control the amount of data to be used in jitter separation. The
default value is (# TIE Points)/Nbps, and in most cases this would work. But if increased
control is required over the number of bits to be used, this argument can be set to a
different value.
RJBWMode Jitter analysis uses a spectral technique to separate RJ from PJ. In the RJ, PJ
Spectrum the noise floor or baseline depicts RJ. The narrow spikes above RJ depict PJ (see
RJ, PJ Spectrum graph). This separation works well for wide bandwidth RJ, having a
uniform PSD across the entire jitter spectrum. But in some cases, this is not the norm and
the PJ components appear much broader. In such cases PJ can be mis-represented as RJ
and this affects the TJ (since TJ is a multiplier of RJ). Setting RJ bandwidth mode to Wide
or White treats RJ as flat. See References (expmeas) for more information.
Defined in
$HPEESOF_DIR/expressions/ael/JitAnalysis.ael
See Also
jitter_separation() (expmeas)
Notes and Equations
1. Default value for Nbps = 2 * Minimum # Whole Pattern per sequence * Nbpp = 2 *
64 * Nbpp
For Periodic data type if the number of whole pattern per sequence, Nwpps = Nbps /
Ntpp, is less than 64, the method used for RJPJ Separation is random (which is
different than the data type or pattern being random). For PRBS15 if Nbps=60000,
Ntpp=16384, NTIEs=2621359 then Nwpps=3. If the number of sequences to use is
less than minimum number of sequences needed for DDJ separation, MinSeqsDDJ =
100/Nwpps, then DDJ cannot be separated and the initial sequences are not used.
For example if Nwpps=3, then MinSeqsDDJ =100/3 = 34. In this case, increase the
number of TIE to (MinSeqsDDJ+1) * Nbps.
Some calculations for the PRBS15 example are shown below:
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Measurement Expressions
Nbps = BitMultiplier * Nbpp
Nwpps = floor(Nbps/Ntpp)
MinSeqsDDJ = ceil(100/Nwpps)
MinNTIEs = (MinSeqsDDJ + 1) * Nbps
MinNSeqs = floor(NTIEs/Nbps)
MaxNSeqs = MinNTIEs/Nbps
Where:
MinNTIEs is the minimum number of TIEs that are needed if the corresponding
number of Nbps is used.
MinSeqsDDJ is the minimum number of sequences that are needed for a successful
DDJ separation.
MinNSeqs is the minimum number of sequences that can be used for given NTIEs.
MaxNSeqs is the maximum number of sequences that can be used for given
MinSeqsDDJ.
So in the above example, if Nbps = 13 * Nbpp = 425971, then Nwpps = 25.
For this Nbps, the minimum number of sequences that can be used for a valid DDJ
separation is 4. This is less than the number of sequences, 6 that is possible with
NTIEs= 2621359. So a valid DDJ separation can be done. In the table below, for
Nwpps ≤63 the RJPJ separation used is random. For Nwpps ≥64, the RJPJ separation
used is periodic.
BitMultiplier Nbps
Nwpps MinNTIEs MinSeqsDDJ MaxNSeqs MinNSeqs
1
32767
1
3309467
100
101
79
7
229369
13
2064321
8
9
11
13
425971
25
2129855
4
5
6
19
622573
37
2490292
3
4
4
25
819175
49
3276700
3
4
3
31
1015777 61
3047331
2
3
2
32
1048544 63
3145632
2
3
2
34
1114078 67
3342234
2
3
2
36
1179612 71
3538836
2
3
2
38
1245146 75
3735438
2
3
2
40
1310680 79
3932040
2
3
1
In addition the frequency resolution of the RJ, PJ Spectrum is improved by increasing
Nbps. But increasing Nbps can significantly increase the RJ, PJ spectrum calculation
time.
2. NumSeqs default value = (# TIE Points)/Nbps.
In order to get a valid jitter separation the number of data points should be at least
have 32 complete data patterns, otherwise jitter separation would terminate with an
error. With number of bits between 32 and 128, jitter separation will be performed,
but the results are questionable. For accurate results, use at least 128 patterns.
Since the separation algorithm is a statistical procedure, the results would correlate
better with more patterns.
PJ is separated from RJ by inspecting the spectral content of jitter. The robustness of this
separation methodology depends on having sufficient frequency resolution in the jitter
spectrum. When the frequency resolution drops below a threshold it could start to cause a
reduction in RJ/PJ separation accuracy. This happens when the number of complete data
patterns in the serial data falls below 128 patterns. When this happens, examine the RJ,
PJ spectrum. If the spectrum is comprised primarily of random noise with very few tall PJ
spikes, then the questionable results are accurate. If there are a large number of PJ spikes
then the jitter measurement should be repeated several times while varying the sequence
185
Measurement Expressions
record length. If the RJ and PJ results change significantly with record length, then the
results are correct.
jitter_separation()
This function does a jitter analysis and separates the jitter components.
Syntax
JitRes = jitter_separation(vJitterSig, vRefClkSig, Nbpp, BitPeriod, BERLevel, DataType,
Pattern, Nbps, NumSeq, RJBWMode, EdgeType, InterpType, MeasType)
Arguments
Name
Description
Default Range
Type
Required
vJitterSig
time-domain based jittered signal
None
(-∞:∞)
Real
Yes
vRefClk
time-domain based reference clock
signal or bit period
None
(0:∞)
Real
No
Nbpp
number of bits per pattern
None
2 to 2^17
integer
Yes
BitPeriod
bit period
None
0 < BitPeriod < 1e-3
Real
Yes
BERLevel
BER level at which to measure TJ
1e-12
1e-40 < BERLevel < 1e-1 Real
No
DataType
data-type
1
1 (Periodic), 2(Random) † Integer
No
Pattern
bit pattern vector or bit pattern filename
None
0 and 1
Array,
String
No
Nbps
number of bits per sequence
††
[2:Inf]
Integer
No
NumSeq
number of sequences of data to be
used in jitter analysis
†††
[1:Inf]
Integer
No
RJBWMode RJ Bandwidth Mode
1
1(Narrow or Pink), 2(Wide Integer
or White)
No
EdgeType
Data Edge Type
3
1(Rising), 2(Falling),
3(Both)
Integer
No
InterType
Interpolation type for holes in TIE for
jitter spectrum
1
1(None), 2(Linear)
Integer
No
3
††††
Integer
No
MeasType Specifies the jitter components and
graphs to calculate.
† Note that Random data type is not supported in this release.
† † The default for Nbps is 2 * minimum number of whole patterns per sequence * Nbpp.
† † † NumSeq defaults is calculated as number of TIE points/Nbps.
† † † † MeasType can be one of the following:
1 Calculate TJpp,RJrms,DJdd
2 Returns TJpp,RJrms,DJdd,PJdd,PJrms,ISIpp,DCD,DDJpp.
3 In addition to measurements in type 2, calculate TJ,RJPJ,DDJ,DDJR,DDJF Histograms &
Bathtub Plot & DDJ vs Bit
4 In addition to measurements in type 3, calculate RJPJ spectrum.
Examples
The following example does a jitter separation of a jittered signal that uses a
PRBS10 source:
JitRes = jitter_separation(vJitSig, vRefClk, 1023, 50 ps, 1e-12, 1,, 5000,
95,,,4)
The returned value JitRes is a list of 18 different measurements.
TJpp = JitRes[0]
RJrms = JitRes[1]
186
Measurement Expressions
DJdd = JitRes[2]
PJdd = JitRes[3]
PJrms = JitRes[4]
ISIpp = JitRes[5]
DCD = JitRes[6]
DDJpp = JitRes[7]
TJHist = JitRes[8]
RJPJHist = JitRes[9]
DDJHist = JitRes[10]
DDJFHist = JitRes[11]
DDJRHist = JitRes[12]
DataBath = JitRes[13]
MdlBath = JitRes[14]
DataQBath = JitRes[15]
MdlQBath = JitRes[16]
DDJvsBit = JitRes[17]
RJPJSpec = JitRes[18]
Where:
vJitterSig is the time-domain jittered signal. The argument jittered signal is the serial
data (time versus amplitude) used in jitter separation. This signal is used in calculating
the zero crossings, and the serial data is calculated from the zero crossings. If there are
no zero crossings, then jitter separation will terminate with an error message. Currently,
only periodic pattern serial data is supported, and the pattern must be repeatable.
Arbitrary or random serial data is not supported.
vRefClkSig can be a reference clock signal (time versus amplitude) or the bit period. If
the clock signal is given, the zero crossings are used to find the clock serial. This zero
crossing is used along with the zero crossings of the jittered data in calculating the Time
Interval Error (TIE). If the bit period is given, then the clock zero crossings are calculated
from the bit period. If not given, the fourth argument bit period is used.
Nbpp is the pattern length and is required in order to automatically detect the pattern. At
minimum this should be 2 (a clock signal) and a maximum of 217 . Note that for larger
pattern length the number of serial bits needed would be large and jitter separation would
take a long time. See Viewing Results (expmeas) for more information.
BitPeriod = Bit period must be greater than 0 and less than 1e-3.
BERLevel is the level at which to calculate TJ, RJpp. This argument is optional and the
default value is 1e-12. For example if the system is being designed for a BER of 1e-12,
then doing a jitter separation at 1e-12 would calculate the TJ at 1e-12.
Pattern can be an array of 0s and 1s or the name of a file containing the pattern. An
example of a pattern in array format is [1,0,0,0,0,0,0,0,1,0]. A pattern must have a 0 and
a 1. In addition, the minimum pattern is a [0, 1] - a clock signal. If the pattern is given in
a file, the pattern bits must be space separated and in a single line. If pattern is not given,
the pattern is automatically detected from the signal bits. For each sequence of data, the
pattern is detected and compared with the previous sequence patter or the given pattern.
If the pattern matches, that particular sequence of data is used.
Nbps indicates the number of bits-per-acquisition or sequence. Nbps is optional and the
default is 2 * Minimum # Whole Pattern per sequence * Nbpp = 2 * 64 * Nbpp. In most
cases this default value would work, but in some cases this value might need to be set
manually since this argument has a direct bearing on the number of serial bits needed for
a valid jitter separation and the RJPJ separation method. See Viewing Results (expmeas)
for more information.
187
Measurement Expressions
NumSeqs can be used to control the amount of data to be used in jitter separation. The
default value is (# TIE Points)/Nbps, and in most cases this would work. But if increased
control is required over the number of bits to be used, this argument can be set to a
different value.
RJBWMode Jitter analysis uses a spectral technique to separate RJ from PJ. In the RJ, PJ
Spectrum the noise floor or baseline depicts RJ. The narrow spikes above RJ depict PJ (see
RJ, PJ Spectrum graph). This separation works well for wide bandwidth RJ, having a
uniform PSD across the entire jitter spectrum. But in some cases, this is not the norm and
the PJ components appear much broader. In such cases PJ can be mis-represented as RJ
and this affects the TJ (since TJ is a multiplier of RJ). Setting RJ bandwidth mode to Wide
or White treats RJ as flat. See References (expmeas) for more information.
MeasType specifies the jitter components and graphs to be calculated and displayed. There
are four values that can be used for MeasType:
1 (RJ DJ TJ): Calculate TJpp, RJrms, DJdd.
2 (Add PJ DDJ): TJpp, RJrms, DJdd, PJdd, PJrms, ISIpp, DCD, DDJpp
3 (Add Histograms, Bathtub, DDJ versus Bits): Measurements in MeasType=2 + TJ,
RJPJ, DDJ, DDJR, DDJF Histograms, Bathtub graphs, and DDJ versus Bits graph.
4 (Add full RJPJ spectrum): Measurements in mode 3 + RJPJ spectrum.
Note
Type 4 measurements can take an exceptionally long time to complete.
InterType For clock-type signals, the DFT is calculated from the uniformly spaced RJ, PJ
time record, where each value in the RJ, PJ time record corresponds to a voltage transition
in the clock-type waveform. For NRZ data-type signals, the RJ, PJ time record is not
comprised of uniformly spaced jitter values. For these signals, the RJ, PJ time record
contains "holes" caused by consecutive logical ones or zeros. The lack of information
about the jitter at times corresponding to these holes makes it impossible to determine
the true RJ, PJ spectrum.
There are two options for displaying the RJ, PJ spectrum. If InterType , the Data TIE
Interpolation mode is set to none, then the spectrum is calculated as if the holes were all
set to a value of zero. In this case, the resulting spectrum appears to be modulated
(convolved in the frequency domain) by the data pattern. If InterpType is set to linear,
then the spectrum is calculated as if the unknown values (holes) were determined using
linear interpolation. In this second case, the resulting spectrum is calculated by filtering
out the higher possible spectral components with a time-variant low-pass filter.
Defined in
$HPEESOF_DIR/expressions/ael/JitAnalysis.ael
See Also
bathtub() (expmeas)
188
Measurement Expressions
Notes and Equations
1. This function requires the ads_si_verification license.
Caution
Due to memory limitations, large datasets created for performing jitter analysis can cause
instabilities in ADS. This can result in the Data Display window crashing without saving the DDS file.
To avoid losing any setup information, save the DDS file before performing a jitter analysis.
2. Default value for Nbps = 2 * Minimum # Whole Pattern per sequence * Nbpp = 2 *
64 * Nbpp
For Periodic data type if the number of whole pattern per sequence, Nwpps = Nbps /
Ntpp, is less than 64, the method used for RJPJ Separation is random (which is
different than the data type or pattern being random). For PRBS15 if Nbps=60000,
Ntpp=16384, NTIEs=2621359 then Nwpps=3. If the number of sequences to use is
less than minimum number of sequences needed for DDJ separation, MinSeqsDDJ =
100/Nwpps, then DDJ cannot be separated and the initial sequences are not used.
For example if Nwpps=3, then MinSeqsDDJ =100/3 = 34. In this case, increase the
number of TIE to (MinSeqsDDJ+1) * Nbps.
Some calculations for the PRBS15 example are shown below:
Nbps = BitMultiplier * Nbpp
Nwpps = floor(Nbps/Ntpp)
MinSeqsDDJ = ceil(100/Nwpps)
MinNTIEs = (MinSeqsDDJ + 1) * Nbps
MinNSeqs = floor(NTIEs/Nbps)
MaxNSeqs = MinNTIEs/Nbps
Where:
MinNTIEs is the minimum number of TIEs that are needed if the corresponding
number of Nbps is used.
MinSeqsDDJ is the minimum number of sequences that are needed for a successful
DDJ separation.
MinNSeqs is the minimum number of sequences that can be used for given NTIEs.
MaxNSeqs is the maximum number of sequences that can be used for given
MinSeqsDDJ.
So in the above example, if Nbps = 13 * Nbpp = 425971, then Nwpps = 25.
For this Nbps, the minimum number of sequences that can be used for a valid DDJ
separation is 4. This is less than the number of sequences, 6 that is possible with
NTIEs= 2621359. So a valid DDJ separation can be done. In the table below, for
Nwpps 63 the RJPJ separation used is random. For Nwpps 64, the RJPJ separation
used is periodic.
BitMultiplier Nbps
Nwpps MinNTIEs MinSeqsDDJ MaxNSeqs MinNSeqs
1
32767
1
3309467
100
101
79
7
229369
13
2064321
8
9
11
13
425971
25
2129855
4
5
6
19
622573
37
2490292
3
4
4
25
819175
49
3276700
3
4
3
31
1015777 61
3047331
2
3
2
32
1048544 63
3145632
2
3
2
34
1114078 67
3342234
2
3
2
36
1179612 71
3538836
2
3
2
38
1245146 75
3735438
2
3
2
40
1310680 79
3932040
2
3
1
In addition the frequency resolution of the RJ, PJ Spectrum is improved by increasing
189
Measurement Expressions
Nbps. But increasing Nbps can significantly increase the RJ, PJ spectrum calculation
time.
3. NumSeqs default value = (# TIE Points)/Nbps.
In order to get a valid jitter separation the number of data points should be at least
have 32 complete data patterns, otherwise jitter separation would terminate with an
error. With number of bits between 32 and 128, jitter separation will be performed,
but the results are questionable. For accurate results, use at least 128 patterns.
Since the separation algorithm is a statistical procedure, the results would correlate
better with more patterns.
4. PJ is separated from RJ by inspecting the spectral content of jitter. The robustness of
this separation methodology depends on having sufficient frequency resolution in the
jitter spectrum. When the frequency resolution drops below a threshold it could start
to cause a reduction in RJ/PJ separation accuracy. This happens when the number of
complete data patterns in the serial data falls below 128 patterns. When this
happens, examine the RJ, PJ spectrum. If the spectrum is comprised primarily of
random noise with very few tall PJ spikes, then the questionable results are accurate.
If there are a large number of PJ spikes then the jitter measurement should be
repeated several times while varying the sequence record length. If the RJ and PJ
results change significantly with record length, then the results are correct.
5. Jitter separation algorithms are sensitive to input parameters in the following ways:
Accurate Bit period is essential in determining the Time Interval Errors. Linear
interpolation is used to determine the threshold crossing, and linear regression
is used to determine the bit period/frequency and phase of the input jittered
signal. The Agilent Infinium oscilloscopes use sinc() interpolation to detect
threshold crossings which is much more accurate than the interpolation method
used in jitter_separation(). In some cases, with the same input signal, results
from the oscilloscope and from jitter_separation() in ADS may be different.
In general it is better to use a longer signal sequence per acquisition (Nbps) to
increase confidence in the separation results. Longer sequences help to acquire
more information about the low-frequency components of jitter.
In some cases, the jitter separation function may produce different results for
the same input signal when treating it as a Periodic Sequence compared to
treating it as an Arbitrary Sequence. One of the major contributors to any such
difference is the length of each sequence. When the sequence is longer, the
results are more similar.
190
Measurement Expressions
Math Functions For Measurement Expressions
This section describes the math functions in detail. The functions are listed in alphabetical
order.
abs() Measurement (expmeas)
acos() Measurement (expmeas)
acosh() Measurement (expmeas)
acot() Measurement (expmeas)
acoth() Measurement (expmeas)
asin() Measurement (expmeas)
asinh() Measurement (expmeas)
atan2() Measurement (expmeas)
atan() Measurement (expmeas)
atanh() Measurement (expmeas)
ceil() Measurement (expmeas)
cint() Measurement (expmeas)
cmplx() Measurement (expmeas)
complex() Measurement (expmeas)
conj() Measurement (expmeas)
convBin() Measurement (expmeas)
convHex() Measurement (expmeas)
convInt() (expmeas)
convOct() Measurement (expmeas)
cos() Measurement (expmeas)
cosh() Measurement (expmeas)
cot() Measurement (expmeas)
coth() Measurement (expmeas)
cum prod() (expmeas)
cum sum() (expmeas)
db() Measurement (expmeas)
dbm() Measurement (expmeas)
dbmtow() Measurement (expmeas)
deg() Measurement (expmeas)
diagonal() (expmeas)
diff() (expmeas)
erf() (expmeas)
erfc() (expmeas)
erfcinv() (expmeas)
erfinv() (expmeas)
exp() Measurement (expmeas)
fft() (expmeas)
fix() Measurement (expmeas)
float() Measurement (expmeas)
floor() Measurement (expmeas)
fmod() Measurement (expmeas)
hypot() Measurement (expmeas)
identity() (expmeas)
im() Measurement (expmeas)
imag() Measurement (expmeas)
int() Measurement (expmeas)
integrate() (expmeas)
interp() (expmeas)
191
Measurement Expressions
interpolate() (expmeas)
inverse() (expmeas)
jn() Measurement (expmeas)
ln() Measurement (expmeas)
log10() Measurement (expmeas)
log() Measurement (expmeas)
mag() Measurement (expmeas)
max2() Measurement (expmeas)
max() Measurement (expmeas)
max outer() (expmeas)
min2() Measurement (expmeas)
min() Measurement (expmeas)
min outer() (expmeas)
num() Measurement (expmeas)
ones() (expmeas)
phase() Measurement (expmeas)
phasedeg() Measurement (expmeas)
phaserad() Measurement (expmeas)
polar() Measurement (expmeas)
pow() Measurement (expmeas)
prod() (expmeas)
rad() Measurement (expmeas)
re() Measurement (expmeas)
real() Measurement (expmeas)
rms() (expmeas)
round() Measurement (expmeas)
sgn() Measurement (expmeas)
sin() Measurement (expmeas)
sinc() Measurement (expmeas)
sinh() Measurement (expmeas)
sqr() (expmeas)
sqrt() Measurement (expmeas)
step() Measurement (expmeas)
sum() Measurement (expmeas)
tan() Measurement (expmeas)
tanh() Measurement (expmeas)
transpose() (expmeas)
wtodbm() Measurement (expmeas)
xor() Measurement (expmeas)
zeros() (expmeas)
Note
You can generally use these functions with data from any type of analysis. They consist of traditional math
(e.g., trigonometric functions and matrix operations) and other functions.
abs()
Returns the absolute value of a integer, real or complex number
Syntax
y = abs(x)
192
Measurement Expressions
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
Integer, real, complex Yes
Examples
a = abs(-45) returns 45
Defined in
Built in
See Also
cint() (expmeas), exp() (expmeas), float() (expmeas), int() (expmeas), log() (expmeas),
log10() (expmeas), pow() (expmeas), sgn() (expmeas), sqrt() (expmeas)
Note
The function name abs() is used for more than one type of expression. For comparison, see the Simulator
Expression abs() Expression (expsim) and the AEL Function abs() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
Notes/Equations
In the case of a complex number, the abs function accepts one complex argument and
returns the magnitude of its complex argument as a positive real number.
acos()
Returns the inverse cosine, or arc cosine, in radians
Syntax
y = acos(x)
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
Integer, real, complex Yes
Examples
a = acos(-1) returns 3.142
Defined in
Built in
193
Measurement Expressions
See Also
asin() (expmeas), atan() (expmeas), atan2() (expmeas)
Note
The function name acos() is used for more than one type of expression. For comparison, see the Simulator
Expression acos() Expression (expsim) and the AEL Function acos() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
Notes/Equations
Returned value ranges from 0 to pi.
acosh()
Returns the inverse hyperbolic cosine
Syntax
y = acosh(x)
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
Integer, real, complex Yes
Examples
a = acosh(1.5) returns 0.962
Defined in
Built in
See Also
acos() (expmeas), asin() (expmeas), atan() (expmeas), atan2() (expmeas)
Note
The function name acosh() is used for more than one type of expression. For comparison, see the
Simulator Expression acosh() Expression (expsim) and the AEL Function acosh() Function (ael). Also, for
more information on the different expression types and the contexts in which they are used, see
Duplicated Expression Names (expmeas).
acot()
Returns the inverse cotangent
194
Measurement Expressions
Syntax
y = acot(x)
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
Integer, real, complex Yes
Examples
a = acot(1.5) returns 0.588
Defined in
Built in
See Also
asin() (expmeas), atan() (expmeas), atan2() (expmeas)
Note
The function name acot() is used for more than one type of expression. For comparison, see the AEL
Function acot() Function (ael). Also, for more information on the different expression types and the
contexts in which they are used, see Duplicated Expression Names (expmeas).
acoth()
Returns the inverse hyperbolic cotangent
Syntax
y = acoth(x)
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
Integer, real, complex Yes
Examples
a = acoth(1.5) returns 0.805
Defined in
Built in
See Also
195
Measurement Expressions
acot() (expmeas), asin() (expmeas), atan() (expmeas), atan2() (expmeas)
Note
The function name acoth() is used for more than one type of expression. For comparison, see the AEL
Function acoth() Function (ael). Also, for more information on the different expression types and the
contexts in which they are used, see Duplicated Expression Names (expmeas).
asin()
Returns the inverse sine, or arc sine, in radians
Syntax
y = asin(x)
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
Integer, real, complex Yes
Examples
a = asin(-1) returns -1.571
Defined in
Built in
See Also
acos() (expmeas), atan() (expmeas), atan2() (expmeas)
Note
The function name asin() is used for more than one type of expression. For comparison, see the Simulator
Expression asin() Expression (expsim) and the AEL Function asin() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
asinh()
Returns the inverse hyperbolic sine
Syntax
y = asinh(x)
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
Integer, real, complex Yes
Examples
196
Measurement Expressions
a = asinh(.5) returns 0.481
Defined in
Built in
See Also
asin() (expmeas), acos() (expmeas), atan() (expmeas), atan2() (expmeas)
Note
The function name asinh() is used for more than one type of expression. For comparison, see the
Simulator Expression asinh() Expression (expsim). Also, for more information on the different expression
types and the contexts in which they are used, see Duplicated Expression Names (expmeas).
atan2()
Returns the inverse tangent, or arc tangent, of the rectangular coordinates y and x
Syntax
y = atan2(y, x)
Arguments
Name Description Default Range Type
Required
x
number
None
(∞:∞)
Integer, real, complex Yes
y
number
None
(∞:∞)
Integer, real, complex Yes
Examples
a = atan2(1, 0) returns 1.571
Defined in
Built in
See Also
acos() (expmeas), asin() (expmeas), atan() (expmeas)
Notes/Equations
Returned value range is -pi to pi. atan2(0,0) returns -pi/2.
197
Measurement Expressions
Note
The function name atan2() is used for more than one type of expression. For comparison, see the
Simulator Expression atan2() Expression (expsim) and the AEL Function atan2() Function (ael). Also, for
more information on the different expression types and the contexts in which they are used, see
Duplicated Expression Names (expmeas).
atan()
Returns the inverse tangent, or arc tangent, in radians
Syntax
y = atan(x)
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
Integer, real, complex Yes
Examples
a = atan(-1) returns -0.785
Defined in
Built in
See Also
acos() (expmeas), asin() (expmeas), atan2() (expmeas)
Notes/Equations
Returned value range is -pi/2 to pi/2.
Note
The function name atan() is used for more than one type of expression. For comparison, see the Simulator
Expression atan() Expression (expsim) and the AEL Function atan() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
atanh()
Returns the inverse hyperbolic tangent
Syntax
y = atanh(x)
Arguments
198
Measurement Expressions
Name Description Default Range Type
x
number
None
(∞:∞)
Required
Integer, real, complex Yes
Examples
a = atanh(.5) returns 0.549
Defined in
Built in
See Also
acos() (expmeas), asin() (expmeas), atan() (expmeas), atan2() (expmeas)
Notes/Equations
Returned value ranges from 0 to pi.
Note
The function name atanh() is used for more than one type of expression. For comparison, see the
Simulator Expression atanh() Expression (expsim) and the AEL Function atanh() Function (ael). Also, for
more information on the different expression types and the contexts in which they are used, see
Duplicated Expression Names (expmeas).
ceil()
Given a real number, returns the smallest integer not less than its argument; that is, its
argument rounded to the next highest number.
Syntax
y = ceil(x)
Arguments
Name Description Default Range Type Required
x
number
None
(∞:∞)
real
Yes
Examples
a = ceil(5.27) returns 6
Defined in
Built in
199
Measurement Expressions
Note
The function name ceil() is used for more than one type of expression. For comparison, see the Simulator
Expression ceil() Expression (expsim) and the AEL Function ceil() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
cint()
Given a non-integer real number, returns a rounded integer.
Syntax
y = cint(x)
Arguments
Name Description Default Range Type Required
x
number
None
(∞:∞)
real
Yes
Examples
a = cint(45.6) returns 46
a = cint(-10.7) returns -11
Defined in
Built in
See Also
abs() (expmeas), exp() (expmeas), float() (expmeas), int() (expmeas), log() (expmeas),
log10() (expmeas), pow() (expmeas), sgn() (expmeas), sqrt() (expmeas)
Notes/Equations
0.5 rounds up, -0.5 rounds down (up in magnitude).
Note
The function name cint() is used for more than one type of expression. For comparison, see the AEL
Function cint() Function (ael). Also, for more information on the different expression types and the
contexts in which they are used, see Duplicated Expression Names (expmeas).
cmplx()
Returns complex number given real and imaginary
Syntax
y = cmplx(x, y)
200
Measurement Expressions
Arguments
Name Description
Default Range Type
Required
x
real part of complex number
None
(∞:∞)
Integer, Real Yes
y
imaginary part of complex number None
(∞:∞)
Integer, Real Yes
Examples
a = cmplx(2, -1) returns 2 - 1j
Defined in
Built in
See Also
complex() (expmeas), imag() (expmeas), real() (expmeas)
Note
The function name cmplx() is used for more than one type of expression. For comparison, see the AEL
Function cmplx() Function (ael). Also, for more information on the different expression types and the
contexts in which they are used, see Duplicated Expression Names (expmeas).
complex()
Returns complex number given real and imaginary
Syntax
y = complex(x, y)
Arguments
Name Description
Default Range Type
x
real part of complex number
None
(∞:∞)
Integer, Real Yes
y
imaginary part of complex number None
(∞:∞)
Integer, Real Yes
Examples
a = complex(2, -1) returns 2 - 1j
Defined in
$HPEESOF_DIR/expressions/ael/elementary_fun.ael
See Also
201
Required
Measurement Expressions
cmplx() (expmeas), imag() (expmeas), real() (expmeas)
Note
The function name complex() is used for more than one type of expression. For comparison, see the
Simulator Expression complex() Expression (expsim). Also, for more information on the different
expression types and the contexts in which they are used, see Duplicated Expression Names (expmeas).
conj()
Returns the conjugate of a complex number
Syntax
y = conj(x)
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
complex Yes
Examples
a = conj(3-4*j) returns 3.000 + j4.000
or 5.000 / 53.130 in magnitude / degrees
Defined in
Built in
See Also
mag() (expmeas)
Note
The function name conj() is used for more than one type of expression. For comparison, see the Simulator
Expression conj() Expression (expsim) and the AEL Function conj() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
convBin()
Returns a binary string of an integer with n-digits
Syntax
y = convBin(val, num)
Arguments
202
Measurement Expressions
Name Description
Default Range Type
Required
val
integer to be converted to a binary
string
None
(∞:∞)
Integer,
real
Yes
num
number of digits in the binary string
None
[0:∞)
Integer
Yes
Examples
a = convBin(1064, 8) returns 00101000
Defined in
Built in
See Also
convHex() (expmeas), convInt() (expmeas), convOct() (expmeas)
Note
The function name convBin() is used for more than one type of expression. For comparison, see the AEL
Function convBin() Function (ael). Also, for more information on the different expression types and the
contexts in which they are used, see Duplicated Expression Names (expmeas).
convHex()
Returns a hexadecimal string of an integer with n-digits
Syntax
y = convHex(val, num)
Arguments
Name Description
Default Range Type
Required
val
integer to be converted to a hexadecimal string None
(∞:∞)
Integer,
real
Yes
num
number of digits in the hexadecimal string
[0:∞)
Integer
Yes
None
Examples
a = convHex(1064, 8) returns 00000428
Defined in
Built in
See Also
convBin() (expmeas), convOct() (expmeas), convInt() (expmeas)
203
Measurement Expressions
Note
The function name convHex() is used for more than one type of expression. For comparison, see the AEL
Function convHex() Function (ael). Also, for more information on the different expression types and the
contexts in which they are used, see Duplicated Expression Names (expmeas).
convInt()
Returns an integer of a binary, octal or hexadecimal number
Syntax
y = convInt(val, base)
Arguments
Name Description
Default Range Type
Required
val
string representation of the binary, octal or hexadecimal number
to be converted
None
None
String
Yes
base
base of the conversion
None
2,8,16
†
Integer Yes
† base values: 2:binary, 8:octal, 16:hexadecimal
Examples
b2I = convInt("11100", 2) returns 28
o2I = convInt("34", 8) returns 28
h2I = convInt("1c", 16) returns 28
Defined in
Built in
See Also
convBin() (expmeas), convHex() (expmeas), convOct() (expmeas)
convOct()
Returns an octal string of an integer with n-digits
Syntax
y = convOct(val, num)
Arguments
Name Description
Default Range Type
Required
val
integer to be converted to a octal
string
None
(∞:∞)
Integer,
real
Yes
num
number of digits in the octal string
None
[0:∞)
Integer
Yes
Examples
204
Measurement Expressions
a = convOct(1064, 8) returns 00002050
Defined in
Built in
See Also
convBin() (expmeas), convHex() (expmeas), convInt() (expmeas)
Note
The function name convOct() is used for more than one type of expression. For comparison, see the the
AEL Function convOct() Function (ael). Also, for more information on the different expression types and
the contexts in which they are used, see Duplicated Expression Names (expmeas).
cos()
Returns the cosine
Syntax
y = cos(x)
Arguments
Name Description
x
Default Range Type
number in radians None
(∞:∞)
Required
Integer, real, complex Yes
Examples
y = cos(pi/3) returns 0.500
Defined in
Built in
See Also
sin() (expmeas), tan() (expmeas)
Note
The function name cos() is used for more than one type of expression. For comparison, see the Simulator
Expression cos() Expression (expsim) and the AEL Function cos() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
cosh()
205
Measurement Expressions
Returns the hyperbolic cosine
Syntax
y = cosh(x)
Arguments
Name Description
x
Default Range Type
number in radians None
(∞:∞)
Required
Integer, real, complex Yes
Examples
y = cosh(0) returns 1
y = cosh(1) returns 1.543
Defined in
Built in
See Also
sinh() (expmeas), tanh() (expmeas)
Note
The function name cosh() is used for more than one type of expression. For comparison, see the Simulator
Expression cosh() Expression (expsim) and the AEL Function cosh() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
cot()
Returns the cotangent
Syntax
y = cot(x)
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
Integer, real, complex Yes
Examples
a = cot(1.5) returns 0.071
Defined in
Built in
206
Measurement Expressions
See Also
tan() (expmeas), tanh() (expmeas)
Note
The function name cot() is used for more than one type of expression. For comparison, see the Simulator
Expression cot() Expression (expsim) and the AEL Function cot() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
coth()
Returns the hyperbolic cotangent
Syntax
y = coth(x)
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
Integer, real, complex Yes
Examples
a = coth(1.5) returns 1.105
Defined in
Built in
See Also
cot() (expmeas), tan() (expmeas), tanh() (expmeas)
Note
The function name coth() is used for more than one type of expression. For comparison, see the Simulator
Expression coth() Expression (expsim) and the AEL Function coth() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
cum_prod()
Returns the cumulative product
Syntax
y = cum_prod(x)
Arguments
207
Measurement Expressions
Name Description
Default Range Type
Required
x
None
Yes
data to find cumulative
product
(∞:∞) Integer, real or
complex
Examples
y = cum_prod(1) returns 1.000
y = cum_prod([1, 2, 3]) returns [1.000, 2.000, 6.000]
y = cum_prod([i, i]) returns [i, i2]
Defined in
Built in
See Also
cum_sum() (expmeas), max() (expmeas), mean() (expmeas), min() (expmeas), prod()
(expmeas), sum() (expmeas)
cum_sum()
Returns the cumulative sum
Syntax
y = cum_sum(x)
Arguments
Name Description
x
Default Range Type
data to find cumulative sum None
(∞:∞)
Integer, real or
complex
Required
Yes
Examples
y = cum_sum([1, 2, 3]) returns [1.000, 3.000, 6.000]
y = cum_sum([i, i] returns [i,2i]
Defined in
Built in
See Also
cum_prod() (expmeas), max() (expmeas), mean() (expmeas), min() (expmeas), prod()
(expmeas), sum() (expmeas)
db()
Returns the decibel measure of a voltage ratio
208
Measurement Expressions
Syntax
y = db(r, z1, z2)
Arguments
Name Description
Default Range Type
Required
r
voltage ratio (vOut/vIn) None
(∞:∞)
Integer, real, complex Yes
z1
source impedance
50.0
(∞:∞)
Integer, real, complex No
z2
load impedance
50.0
(∞:∞)
Integer, real, complex No
Examples
y = db(100) returns 40
y = db(8-6*j) returns 20
Defined in
Built in
See Also
dbm() (expmeas), pae() (expmeas)
Notes/Equations
dbValue = 20 log(mag(r)) - 10 log(zOutfactor/zInfactor)
zOutfactor = mag(z2)**2 / real (z2)
zInfactor = mag(z1)**2 / real (z1).
Note
The function name db() is used for more than one type of expression. For comparison, see the Simulator
Expression db() Expression (expsim) and the AEL Function dB() Function (ael). Also, for more information
on the different expression types and the contexts in which they are used, see Duplicated Expression
Names (expmeas).
dbm()
Returns the decibel measure of a voltage referenced to a 1 milliwatt signal
Syntax
y = dbm(v, z)
Arguments
209
Measurement Expressions
Name Description
Default Range Type
Required
v
voltage (the peak
voltage)
None
(∞:∞)
Integer, real, complex Yes
z
impedance
50.0
(∞:∞)
Integer, real, complex No
Examples
y = dbm(100) returns 50
y = dbm(8-6*j) returns 30
Defined in
Built in
See Also
db() (expmeas), pae() (expmeas)
Notes/Equations
The voltage is assumed to be a peak value. Signal voltages stored in the dataset from AC
and harmonic balance simulations are in peak volts. However, noise voltages obtained
from AC and HB simulations are in rms volts. Using the dbm() function with noise voltages
will yield a result that is 3 dB too low unless the noise voltage is first converted to peak:
noise_power = dbm(vout.noise * sqrt(2));
Understanding the dbm() Function
Given a power Po in Watts, the power in dB is:
Po_dBW = 10*log(mag(Po/(1 W)))
while the power in dBm is:
Po_dBm =
=
10*log(mag(Po/(1 W)))+ 30
=
Po_dB + 30
10*log(mag(Po/(1 mW)))
Given a voltage Vo in Volts, the voltage in dB is:
V_dBV = 20*log(mag((Vo/(1 V)))
This is the db() (expmeas) function - voltage in dB relative to 1V. Although dB is a
dimensionless quantity, it is normal to attach dB to a value in order to differentiate it from
the absolute value.
Given a real impedance Zo, the power-voltage relation is:
210
Measurement Expressions
Po = (Vo) 2/(2*Zo)
Using the above, Po in dBm is then:
Po_dBm =
10*log(mag(Po/(1 W))) + 30
=
10*log(mag((Vo/(1 V)) 2/(2*Zo/(1 Ohm)))) + 30
=
10*log(mag((Vo/(1 V)) 2)) - 10*log(mag(2*Zo/(1 Ohm))) + 30
=
20*log(mag(Vo/(1 V))) - 10*log(mag(Zo/(50 Ohm))) + 10
This is the dbm() function - voltage in dBm in a Zo environment.
Note
The function name dbm() is used for more than one type of expression. For comparison, see the Simulator
Expression dbm() Expression (expsim) and the AEL Function dBm() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
dbmtow()
Converts dBm to watts
Syntax
wValue = dbmtow(P)
Arguments
Name Description
P
Default Range Type Required
power expressed in dBm None
[0:∞)
Real Yes
Examples
y = dbmtow(0) returns .001 W
y = dbmtow(-10) returns 1.000E-4 W
Defined in
$HPEESOF_DIR/expressions/ael/elementary_fun.ael
See Also
dbm() (expmeas), wtodbm() (expmeas)
Note
The function name dbmtow() is used for more than one type of expression. For comparison, see the
Simulator Expression dbmtow() Expression (expsim). Also, for more information on the different
expression types and the contexts in which they are used, see Duplicated Expression Names (expmeas).
deg()
Converts radians to degrees
211
Measurement Expressions
Syntax
y = deg(x)
Arguments
Name Description
x
Default Range Type
number in radians None
(∞:∞)
Required
Integer, Real Yes
Examples
y = deg(1.5708) returns 90
y = deg(pi) returns 180
Defined in
Built in
See Also
rad() (expmeas)
Note
The function name deg() is used for more than one type of expression. For comparison, see the Simulator
Expression deg() Expression (expsim) and the AEL Function deg() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
diagonal()
Returns the diagonal of a square matrix as a matrix
Syntax
y = diagonal(Matrix)
Arguments
Name Description
Default Range Type
Required
Matrix square matrix to find the
diagonal
None
Yes
(∞:∞)
Integer, Real or
Complex
Examples
mat={{1,2,3},{4,5,6},{7,8,9}}
diag=diagonal(mat) returns {1,5,9}
For a 2-port S-parameter analysis of 10 freq points:
diagS=diagonal(S) would return S11 and S22 for each frequency point
Defined in
Built In
212
Measurement Expressions
See Also
transpose() (expmeas), inverse() (expmeas)
diff()
Calculates the simple numerical first derivative. Can be used to calculate group delay.
Syntax
y = diff(data, pad)
Arguments
Name Description
Default Range Type
data
data to find numerical derivative
None
(∞:∞)
pad
pad the differentiated data with an extra
value
0
[0:1] † Integer
Required
Real, Complex Yes
No
† If pad is 1, then the differentiated data is padded with an extra value (last value of
differentiated data) to make it the same length as the data to be differentiated. If 0
(default) then the length of the differentiated data is one less than the length of data to
be differentiated.
Examples
group_delay = -diff(unwrap(phaserad(S21),pi))/(2*pi)
Defined in
$HPEESOF_DIR/expressions/ael/elementary_fun.ael
See Also
dev_lin_phase() (expmeas), integrate() (expmeas), phasedeg() (expmeas), phaserad()
(expmeas), ripple() (expmeas), unwrap() (expmeas)
Notes/Equations
This function calculates the first derivative of the dependent data with respect to the inner
independent value i.e. dy/dx. The function uses the simple forward finite-divideddifference formulas of 2 values. The error is O(h), where h is the independent step size.
The error decreases with smaller values of h. If the data to be differentiated does not have
an explicit independent-name, the differentiated data is given an independent name
"diffX'.
erf()
213
Measurement Expressions
Calculates the error function, the area under the Gaussian curve exp(-x**2)
Syntax
y = erf(x)
Arguments
Name Description Default Range Type
Required
x
Yes
number
None
(∞:∞)
Integer,
real
Examples
a = -erf(0.1) returns 0.112
a = -erf(0.2) returns 0.223
Defined in
Built in
See Also
erfc() (expmeas)
erfc()
Calculates the complementary error function, or 1 minus the error function. For large x,
this can be calculated more accurately than the plain error function
Syntax
y = erfc(x)
Arguments
Name Description Default Range Type
Required
x
Yes
number
None
(∞:∞)
Integer,
real
Examples
a = erfc(0.1) returns 0.888
a = erfc(0.2) returns 0.777
Defined in
Built in
See Also
214
Measurement Expressions
erf() (expmeas)
erfcinv()
Returns the inverse complementary error function as a real number
Syntax
y = erfcinv(x)
Arguments
Name Description Default Range Type
Required
x
Yes
number
None
[0:2] † Integer,
real
† For numbers outside the range, erfcinv returns <-+∞>. If val is 0, erfcinv returns <∞>.
If val is 2, then <-∞>
Examples
res= erfcinv(0.5) returns 0.477
res= erfcinv(1.9) returns -1.163
Defined in
Built In
See Also
erfc() (expmeas)
erfinv()
Returns the inverse error function as a real number
Syntax
y = erfinv(x)
Arguments
Name Description Default Range Type
Required
x
Yes
number
None
[-1:1]
†
Integer,
real
† For numbers outside the range, erfinv returns <-+∞>. If x is +1, erfinv returns <∞>. If
x is -1, then <-∞>.
Examples
215
Measurement Expressions
res= erfinv(-0.4) returns -0.371
res= erfinv(0.8) returns 0.906
Defined in
Built In
See Also
erf() (expmeas)
exp()
The exponential function is used to calculate powers of e. Given a complex number, x, the
exp(x) function calculates e to the power of x (i.e. ex)
Syntax
y = exp(x)
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
Integer, real, complex Yes
Examples
a = exp(1) returns 2.71828
b = exp(1+j1) returns 1.469 + j*2.287
Defined in
Built in
See Also
abs() (expmeas), cint() (expmeas), float() (expmeas), int() (expmeas), log() (expmeas),
log10() (expmeas), pow() (expmeas), sgn() (expmeas), sqrt() (expmeas)
Notes/Equations
If
x = a+j*b
then
ex = ea+j*b = (ea)*(ej*b) = (ea)*(cos(b)+j*sin(b))
216
Measurement Expressions
Note
The function name exp() is used for more than one type of expression. For comparison, see the Simulator
Expression exp() Expression (expsim) and the AEL Function exp() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
fft()
Performs the discrete Fourier transform
Syntax
y = fft(x, length)
Arguments
Name Description
x
Default Range Type
Required
data to be transformed None
(∞:∞)
Integer, real, complex Yes
length length of the transform None
[1:∞)
Integer
Yes
Examples
fft([1, 1, 1, 1]) returns [4+0i, 0+0i]
fft([1, 0, 0, 0] returns [1+0i, 1+0i]
fft(1, 4) returns [1+0i, 1+0i]
Defined in
Built in
See Also
fs() (expmeas), ts() (expmeas)
Notes/Equations
The fft() function uses a high-speed radix-2 fast Fourier transform when the length of x is
a power of two. fft(x, n) performs an n-point discrete Fourier transform, truncating x if
length(x) > n and padding x with zeros if length(x) < n.
fft() uses a real transform if x is real and a complex transform if x is complex. If the
length of x is not a power of two, then a mixed radix algorithm based on the prime factors
of the length of x is used.
The fft() function is designed to work with uniformly spaced waveforms. If a non-uniform
waveform is input, then the output spectrum will be incorrect. For non-uniformly spaced
data, use the fs() function.
fix()
Takes a real number argument, truncates it, and returns an integer value
217
Measurement Expressions
Syntax
y = fix(x)
Arguments
Name Description Default Range Type
Required
x
Yes
number
None
(∞:∞)
Integer,
real
Examples
a = fix(5.9) returns 5
Defined in
Built in
Note
The function name fix() is used for more than one type of expression. For comparison, see the AEL
Function fix() Function (ael). Also, for more information on the different expression types and the contexts
in which they are used, see Duplicated Expression Names (expmeas).
float()
Converts an integer to a real (floating-point) number
Syntax
y = float(x)
Arguments
Name Description
x
Default Range Type
number to convert None
(∞:∞)
Required
Integer Yes
Examples
a = float(10)
Defined in
Built in
See Also
abs() (expmeas), cint() (expmeas), int() (expmeas), log10() (expmeas), pow()
(expmeas), sgn() (expmeas), sqrt() (expmeas)
218
Measurement Expressions
Note
The function name float() is used for more than one type of expression. For comparison, see the AEL
Function float() Function (ael). Also, for more information on the different expression types and the
contexts in which they are used, see Duplicated Expression Names (expmeas).
floor()
Returns the largest integer not more than its argument from a real number
Syntax
y = floor(x)
Arguments
Name Description
x
Default Range Type Required
number to convert None
(∞:∞)
Real Yes
Examples
a = floor(4.3) returns 4
Defined in
Built in
Note
The function name floor() is used for more than one type of expression. For comparison, see the Simulator
Expression floor() Expression (expsim) and the AEL Function floor() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
fmod()
Returns the remainder of the division of two real numbers
Syntax
y = fmod(fNum, fDenom)
Arguments
Name
Description
Default Range Type
Required
fNum
Value of numerator
None
(∞:∞)
Integer, Real Yes
fDenom Value of denominator None
(∞:∞)
Integer, Real Yes
Examples
y = fmod(4.2, 2.0) returns 0.2
Defined In
219
Measurement Expressions
$HPEESOF_DIR/expressions/ael/elementary_fun.ael
Note
The function name fmod() is used for more than one type of expression. For comparison, see the
Simulator Expression fmod() Expression (expsim). Also, for more information on the different expression
types and the contexts in which they are used, see Duplicated Expression Names (expmeas).
hypot()
Returns the hypotenuse
Syntax
y = hypot(xVal, yVal)
Arguments
Name Description Default Range Type
Required
xVal
Value of X
None
(∞:∞)
Real, Complex Yes
yVal
Value of Y
None
(∞:∞)
Real, Complex Yes
Examples
y = hypot(2, 1) returns 5
Defined In
$HPEESOF_DIR/expressions/ael/elementary_fun.ael
Note
The function name hypot() is used for more than one type of expression. For comparison, see the
Simulator Expression hypot() Expression (expsim). Also, for more information on the different expression
types and the contexts in which they are used, see Duplicated Expression Names (expmeas).
identity()
Returns the identity matrix
Syntax
y = identity(rows, columns)
Arguments
Name
Description
Default Range Type
rows
number of rows †
None
[i:∞)
Integer Yes
None
[i:∞)
Integer No
columns number of columns
†
Required
† If one argument is supplied, then a square matrix is returned with ones on the diagonal
and zeros elsewhere. If two arguments are supplied, then a matrix with size rows cols is
returned, again with ones on the diagonal.
220
Measurement Expressions
Examples
a = identity(2)
Defined in
Built in
See Also
ones() (expmeas), zeros() (expmeas)
im()
Returns the imaginary component of a complex number
Syntax
y = im(x)
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
complex Yes
Examples
y = imag(1-1*j) returns -1.000
Defined in
Built in
See Also
imag() (expmeas), cmplx() (expmeas), real() (expmeas)
Note
The function name im() is used for more than one type of expression. For comparison, see the AEL
Function im() Function (ael). Also, for more information on the different expression types and the contexts
in which they are used, see Duplicated Expression Names (expmeas).
imag()
Returns the imaginary component of a complex number
Syntax
y = imag(x)
221
Measurement Expressions
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
complex Yes
Examples
y = imag(1-1*j) returns -1.000
Defined in
Built in
See Also
cmplx() (expmeas), im() (expmeas), real() (expmeas)
Note
The function name imag() is used for more than one type of expression. For comparison, see the
Simulator Expression imag() Expression (expsim) and the AEL Function imag() Function (ael). Also, for
more information on the different expression types and the contexts in which they are used, see
Duplicated Expression Names (expmeas).
int()
Converts an real to an integer
Syntax
y = int(x)
Arguments
Name Description
x
Default Range Type Required
number to convert None
(∞:∞)
Real Yes
Examples
a = int(4.3) returns 4
b = int(334.235) returns integer 334
c = int(-.45e3) returns integer -450
Defined in
Built in
222
Measurement Expressions
See Also
abs() (expmeas), cint() (expmeas), exp() (expmeas), float() (expmeas), log10()
(expmeas), pow() (expmeas), sgn() (expmeas), sqrt() (expmeas)
Note
The function name int() is used for more than one type of expression. For comparison, see the Simulator
Expression int() Expression (expsim) and the AEL Function int() Function (ael). Also, for more information
on the different expression types and the contexts in which they are used, see Duplicated Expression
Names (expmeas).
integrate()
Returns the integral of data
Syntax
y = integrate(data, start, stop, incr)
Arguments
Name Description
Default
Range Type
Required
data
data to be intergated
None
(∞:∞)
Integer, real
Yes
start
starting value of the
integration
first point in the data
(∞:∞)
Integer, real
No
stop
stop value of the integration
last point in the data
(∞:∞)
Integer, real
†
No
incr
increment
(stop - start)/(# data points - 1) [0:∞)
Integer, real
No
† stop can be an array.
Examples
x = [0::0.01::1.0]
y = vs(2*exp(-x*x) / sqrt(pi), x)
z= integrate(y, 0.1, 0.6, 0.001) returns 0.491
xx=[1::0.1::2]
yy=vs(sin(xx),xx)
Stop=[1.9,2.0]
intgYY=integrate(yy,1,Stop,0.1) returns [0.767, 0.958]
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
diff() (expmeas)
223
Measurement Expressions
Notes/Equations
Returns the integral of data from start to stop with increment incr using the composite
trapezoidal rule on uniform subintervals. The Stop limit can be an array of values. In this
case, the function returns integration for limits [start, stop[0]], [start, stop[1]], etc.
If no incr parameter is given, then no increment (or no interpolation) will be performed.
interp()
Returns linearly interpolated data between start and stop with increment.
Syntax
y = interp(Data, Start, Stop, Increment)
Arguments
Name
Description
Default
Range Type
Required
Data
Data to be interpolated
None
(∞:∞)
Integer,
Real
Yes
Start
Independent value specifying start
First data point
(∞:∞)
Integer,
Real
No
Stop
Independent value specifying stop
Last data point
(∞:∞)
Integer,
Real
No
(StopStart)/(NumDataPoints-1)
(0:∞)
Integer,
Real
No
Increment Increment between interpolated
data points
Examples
x=[1::0.5::2]
y=vs(sin(x),x)
interpP=interp(y,1,1.5,0.1) returns
1.0 0.841
1.1 0.873
1.2 0.904
1.3 0.935
1.4 0.966
1.5 0.997
y = interp(Data, Start, Stop, Increment)
Defined in
Built in
See also
interpolate() (expmeas)
interpolate()
Interpolates data
Syntax
224
Measurement Expressions
Syntax
y = interpolate(InterpType,Data,iVar1,iVal1,iVar2,iVal2,....,iVarN,iValN)
Arguments
Name
Description
Default Range
Type
Required
InterpType
Type of interpolation
None
"linear", "cubic",
"spline"
String
Yes
Data
Data to interpolate
None
None
Integer,
Real
Yes
iVar1,
iVar2,...
Dimension of independent variable to
interpolate
None
None
Integer
Yes
iVal1,
iVal2,...
values to interpolate
None
None
Integer,
real
Yes
Examples
linI = interpolate("linear", colY, 1,[1::0.5::4])
cubicI = interpolate("cubic", colY, 1,[1::0.2::2])
splineI = interpolate("spline", colY, 1,[-2::0.2::2])
For a 2-D data with 2 independents, the following interpolates dimension 1
(inner-most)
from 1 to 4 in steps of 0.5 and second dimension at 0.5:
linI = interpolate("linear", colY, 1,[1::0.5::4],2,0.5)
Defined in
Built in
See also
interp() (expmeas)
Notes/Equations
This function can interpolate data over multiple dimensions.
inverse()
Returns the inverse of a matrix
Syntax
y = inverse(Matrix)
Arguments
Name Description
Default Range Type
Matrix square matrix to find the inverse None
(∞:∞)
Integer, Real or
Complex
225
Required
Yes
Measurement Expressions
Examples
inverse({{1, 2}, {3, 4) returns -2, 1}, {1.5, -0.5}}
Defined in
Built in
See Also
diagonal() (expmeas), transpose() (expmeas)
jn()
Computes the Bessel function of the first kind and returns a real number
Syntax
y = jn(n, x)
Arguments
Name Description
Default Range Type
Required
n
order
None
(∞:∞)
Integer Yes
x
value for which the Bessel value is to be found None
(∞:∞)
Real
Yes
Examples
jn0_15 = jn(0, 15) returns -0.014
jn1_xV = jn(1, 5.23) returns -0.344
jn10_15 = jn(10, 15) returns -0.09
Defined in
in-built
Note
The function name jn() is used for more than one type of expression. For comparison, see the Simulator
Expression jn() Expression (expsim). Also, for more information on the different expression types and the
contexts in which they are used, see Duplicated Expression Names (expmeas).
ln()
Returns the natural logarithm (ln)
Syntax
y = ln(x)
Arguments
226
Measurement Expressions
Name Description Default Range Type
x
number
None
(∞:∞)
Required
Integer, real, complex Yes
Examples
a = ln(e) returns 1
Defined in
Built in
See Also
abs() (expmeas), cint() (expmeas), exp() (expmeas), float() (expmeas), int() (expmeas),
pow() (expmeas), sgn() (expmeas), sqrt() (expmeas)
Note
The function name ln() is used for more than one type of expression. For comparison, see the Simulator
Expression ln() Expression (expsim) and the AEL Function ln() Function (ael). Also, for more information
on the different expression types and the contexts in which they are used, see Duplicated Expression
Names (expmeas).
log10()
Returns the base 10 logarithm of an integer or real number
Syntax
y = log10(x)
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
Integer, real, complex Yes
Examples
a = log10(10) returns 1
a = log10(0+0i) returns NULL and an error message "log of zero"
Defined in
Built in
See Also
abs() (expmeas), cint() (expmeas), exp() (expmeas), float() (expmeas), int() (expmeas),
227
Measurement Expressions
log() (expmeas), pow() (expmeas), sgn() (expmeas), sqrt() (expmeas)
Note
The function name log10() is used for more than one type of expression. For comparison, see the
Simulator Expression log10() Expression (expsim) and the AEL Function log10() Function (ael). Also, for
more information on the different expression types and the contexts in which they are used, see
Duplicated Expression Names (expmeas).
log()
Returns the base 10 logarithm of an integer or real number
Syntax
y = log(x)
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
Integer, real, complex Yes
Examples
a = log(10) returns 1
a = log(0+0i) returns NULL and an error message "log of zero"
Defined in
Built in
See Also
abs() (expmeas), cint() (expmeas), exp() (expmeas), float() (expmeas), int() (expmeas),
log10() (expmeas), pow() (expmeas), sgn() (expmeas), sqrt() (expmeas)
Note
The function name log() is used for more than one type of expression. For comparison, see the Simulator
Expression log() Expression (expsim) and the AEL Function log() Function (ael). Also, for more information
on the different expression types and the contexts in which they are used, see Duplicated Expression
Names (expmeas).
mag()
Returns the magnitude
Syntax
y = mag(x)
Arguments
228
Measurement Expressions
Name Description Default Range Type
x
number
None
(∞:∞)
Required
Integer, real, complex Yes
Examples
a = mag(3-4*j) returns 5.000
Defined in
Built in
See Also
conj() (expmeas)
Note
The function name mag() is used for more than one type of expression. For comparison, see the Simulator
Expression mag() Expression (expsim) and the AEL Function mag() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
max2()
Returns the larger value of two numeric values, or NULL if parameters are invalid
Syntax
y = max2(x, y)
Arguments
Name Description Default Range Type
Required
x
number
None
(∞:∞)
Integer, real, complex Yes
y
number
None
(∞:∞)
Integer, real, complex Yes
Examples
a = max2(1.5, -1.5) returns 1.500
Defined in
Built in
See Also
cum_prod() (expmeas), cum_sum() (expmeas), max() (expmeas), mean() (expmeas),
min() (expmeas), prod() (expmeas), sum() (expmeas)
229
Measurement Expressions
Note
The function name max2() is used for more than one type of expression. For comparison, see the AEL
Function max2() Function (ael). Also, for more information on the different expression types and the
contexts in which they are used, see Duplicated Expression Names (expmeas).
max()
Returns the maximum value.
Syntax
y = max(x)
Arguments
Name Description
x
Default Range Type
data to find max None
(∞:∞)
Required
Integer, real or
complex
Yes
Examples
a = max([1, 2, 3]) returns 3
Defined in
Built in
See Also
cum_prod() (expmeas), cum_sum() (expmeas), max2() (expmeas), mean() (expmeas),
min() (expmeas), prod() (expmeas), sum() (expmeas)
Note
The function name max() is used for more than one type of expression. For comparison, see the Simulator
Expression max() Expression (expsim). Also, for more information on the different expression types and
the contexts in which they are used, see Duplicated Expression Names (expmeas).
max_outer()
Computes the maximum across the outer dimension of two-dimensional data
Syntax
y = max_outer(data)
Arguments
Name Description
Default Range Type
data
None
2-dimensional data to find
max
(∞:∞)
Required
Integer, Real, Complex Yes
Examples
230
Measurement Expressions
y = max_outer(data)
Defined in
$HPEESOF_DIR/expressions/ael/statistcal_fun.ael
See Also
fun_2d_outer() (expmeas), mean_outer() (expmeas), min_outer() (expmeas)
Notes/Equations
The max function operates on the inner dimension of two-dimensional data. The
max_outer function just calls the fun_2d_outer function, with max being the applied
operation. As an example, assume that a Monte Carlo simulation of an amplifier was run,
with 151 random sets of parameter values, and that for each set the S-parameters were
simulated over 26 different frequency points. S21 becomes a [151 Monte Carlo iteration X
26 frequency] matrix, with the inner dimension being frequency, and the outer dimension
being Monte Carlo index. Now, assume that it is desired to know the maximum value of
the S-parameters at each frequency. Inserting an equation max(S21) computes the
maximum value of S21 at each Monte Carlo iteration. If S21 is simulated from 1 to 26
GHz, it computes the maximum value over this frequency range, which usually is not very
useful. Inserting an equation max_outer(S21) computes the maximum value of S21 at
each frequency.
min2()
Returns the lesser value of two numeric values, or NULL if parameters are invalid
Syntax
y = min2(x, y)
Arguments
Name Description Default Range Type
Required
x
number
None
(∞:∞)
Integer, real, complex Yes
y
number
None
(∞:∞)
Integer, real, complex Yes
Examples
a = min2(1.5, -1.5) returns -1.500
Defined in
Built in
231
Measurement Expressions
See Also
cum_prod() (expmeas), cum_sum() (expmeas), max() (expmeas), max2() (ael), mean()
(expmeas), min() (expmeas), prod() (expmeas), sum() (expmeas)
Note
The function name min2() is used for more than one type of expression. For comparison, see the AEL
Function min2() Function (ael). Also, for more information on the different expression types and the
contexts in which they are used, see Duplicated Expression Names (expmeas).
min()
Returns the minimum value.
Syntax
y = min(x)
Arguments
Name Description
x
Default Range Type
data to find min None
(∞:∞)
Required
Integer, real or
complex
Yes
Examples
a = min([1, 2, 3]) returns 1
Defined in
Built in
See Also
cum_prod() (expmeas), cum_sum() (expmeas), max() (expmeas), max2() (expmeas),
mean() (expmeas), prod() (expmeas), sum() (expmeas)
Note
The function name min() is used for more than one type of expression. For comparison, see the Simulator
Expression min() Expression (expsim). Also, for more information on the different expression types and
the contexts in which they are used, see Duplicated Expression Names (expmeas).
min_outer()
Computes the minimum across the outer dimension of two-dimensional data
Syntax
y = min_outer(data)
Arguments
232
Measurement Expressions
Name Description
data
Default Range Type
2-dimensional data to find min None
(∞:∞)
Required
Integer, Real, Complex Yes
Examples
y = min_outer(data)
Defined in
$HPEESOF_DIR/expressions/ael/statistcal_fun.ael
See Also
fun_2d_outer() (expmeas), max_outer() (expmeas), mean_outer() (expmeas)
Notes/Equations
The min function operates on the inner dimension of two-dimensional data. The min_outer
function just calls the fun_2d_outer function, with min being the applied operation. As an
example, assume that a Monte Carlo simulation of an amplifier was run, with 151 random
sets of parameter values, and that for each set the S-parameters were simulated over 26
different frequency points. S21 becomes a [151 Monte Carlo iteration X 26 frequency]
matrix, with the inner dimension being frequency, and the outer dimension being Monte
Carlo index. Now, assume that it is desired to know the minimum value of the Sparameters at each frequency. Inserting an equation min(S21) computes the minimum
value of S21 at each Monte Carlo iteration. If S21 is simulated from 1 to 26 GHz, it
computes the minimum value over this frequency range, which usually is not very useful.
Inserting an equation min_outer(S21) computes the minimum value of S21 at each
frequency.
num()
Returns an integer that represents an ASCII numeric value of the first character in the
specified string.
Syntax
y = num(str)
Arguments
Name Description
str
Default Range Type Required
string to convert to integer None
None
String Yes
Examples
a = num("/users/myhome/fullpath") returns 47
a = num("alpha") returns 97
233
Measurement Expressions
Defined in
Built in
Note
The function name num() is used for more than one type of expression. For comparison, see the AEL
Function num() Function (ael). Also, for more information on the different expression types and the
contexts in which they are used, see Duplicated Expression Names (expmeas).
ones()
Returns ones matrix
Syntax
y = ones(rows, columns)
Arguments
Name
Description
Default Range Type
rows
number of rows †
None
[i:∞)
Integer Yes
None
[i:∞)
Integer No
columns number of columns
†
Required
† If only one argument is supplied, then a square matrix is returned. If two are supplied,
then a matrix of ones with size rows X cols is returned.
Examples
a = ones(2) returns {{1, 1}, {1, 1}}
Defined in
Built in
See Also
identity() (expmeas), zeros() (expmeas)
phase()
Phase in degrees
Syntax
y = phase(x)
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
Complex Yes
Examples
234
Measurement Expressions
a = phase(1*i) returns 90
a = phase(1+1i) returns 45
Defined in
Built-in
See Also
phaserad() (expmeas)
Note
The function name phase() is used for more than one type of expression. For comparison, see the
Simulator Expression phase() Expression (expsim) and the AEL Function phase() Function (ael). Also, for
more information on the different expression types and the contexts in which they are used, see
Duplicated Expression Names (expmeas).
phasedeg()
Phase in degrees
Syntax
y = phasedeg(x)
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
Complex Yes
Examples
a = phasedeg(1*i) returns 90
a = phasedeg(1+1i) returns 45
Defined in
Built-in
See Also
dev_lin_phase() (expmeas), diff() (expmeas), phase() (expmeas), phaserad() (expmeas),
ripple() (expmeas), unwrap() (expmeas)
235
Measurement Expressions
Note
The function name phasedeg() is used for more than one type of expression. For comparison, see the
Simulator Expression phasedeg() Expression (expsim) and the AEL Function phasedeg() Function (ael).
Also, for more information on the different expression types and the contexts in which they are used, see
Duplicated Expression Names (expmeas).
phaserad()
Phase in radians
Syntax
y = phaserad(x)
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
Complex Yes
Examples
a = phaserad(1*i) returns 1.5708
a = phaserad(1+1i) returns 0.785398
Defined in
Built in
See Also
dev_lin_phase() (expmeas), diff() (expmeas), phase() (expmeas), phasedeg() (expmeas),
ripple() (expmeas), unwrap() (expmeas)
Note
The function name phaserad() is used for more than one type of expression. For comparison, see the
Simulator Expression phaserad() Expression (expsim) and the AEL Function phaserad() Function (ael).
Also, for more information on the different expression types and the contexts in which they are used, see
Duplicated Expression Names (expmeas).
polar()
Builds a complex number from magnitude and angle (in degrees)
Syntax
y = polar(mag, angle)
Arguments
236
Measurement Expressions
Name Description
Default Range Type
mag
None
(∞:∞)
Integer, Real Yes
None
(∞:∞)
Integer, Real Yes
magnitude part of complex
number
angle angle part of complex number
Required
Examples
a = polar(1, 90) returns 0+1i
a = polar(1, 45) returns 0.707107+0.707107i
Defined in
Built in
Note
The function name polar() is used for more than one type of expression. For comparison, see the
Simulator Expression polar() Expression (expsim) and the AEL Function polar() Function (ael). Also, for
more information on the different expression types and the contexts in which they are used, see
Duplicated Expression Names (expmeas).
pow()
Raises a number to a given power
Syntax
yPow = pow(x, y)
Arguments
Name Description Default Range Type
Required
x
number
None
(∞:∞)
Integer,
real
Yes
y
exponent
None
(∞:∞)
Integer,
real
Yes
Examples
a = pow(4, 2) returns 16
a = pow(1+j*1,2+j*2) returns -0.266+j*0.32
Defined in
Built in
See Also
abs() (expmeas), cint() (expmeas), exp() (expmeas), float() (expmeas), int() (expmeas),
log10() (expmeas), sgn() (expmeas), sqrt() (expmeas)
237
Measurement Expressions
Note
The function name pow() is used for more than one type of expression. For comparison, see the Simulator
Expression pow() Expression (expsim) and the AEL Function pow() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
prod()
Returns the product
Syntax
y = prod(x)
Arguments
Name Description
Default Range Type
Required
x
None
Yes
data to find
product
(∞:∞) Integer, real or
complex
Examples
a = prod([1, 2, 3] returns 6
a = prod([4, 4, 4]) returns 64
Defined in
Built-in
See Also
sum() (expmeas)
rad()
Converts degrees to radians
Syntax
y = rad(x)
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
Integer, Real Yes
Examples
a = rad(90) returns 1.5708
a = rad(45) returns 0.785398
Defined in
238
Measurement Expressions
Built in
See Also
deg() (expmeas)
Note
The function name rad() is used for more than one type of expression. For comparison, see the Simulator
Expression rad() Expression (expsim) and the AEL Function rad() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
re()
Returns the real component of a complex number
Syntax
y = re(x)
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
complex Yes
Examples
y = re(1-1*j) returns 1.000
Defined in
Built in
See Also
cmplx() (expmeas), imag() (expmeas), real() (expmeas)
Note
The function name re() is used for more than one type of expression. For comparison, see the AEL
Function re() Function (ael). Also, for more information on the different expression types and the contexts
in which they are used, see Duplicated Expression Names (expmeas).
real()
Returns the real component of a complex number
Syntax
y = real(x)
239
Measurement Expressions
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
complex Yes
Examples
y = real(1-1*j) returns 1.000
Defined in
Built in
See Also
cmplx() (expmeas), imag() (expmeas), re() (expmeas)
Note
The function name real() is used for more than one type of expression. For comparison, see the Simulator
Expression real() Expression (expsim) and the AEL Function real() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
rms()
Returns the root mean square value
Syntax
y = rms(Value)
Arguments
Name Description
Default Range Type
Value Value to find RMS None
(∞:∞)
Required
Integer, Real, Complex Yes
Examples
rmsR = rms(2) returns 1.414
rmsR = rms(complex(3, 10)) returns 7.382/73.301
rmsR = rms( [1, 2, 3, 4, 5,] ) returns [0.707, 1.414, 2.121, 2.828, 3.536]
Defined in
$HPEESOF_DIR/expressions/ael/elementary_fun.ael
Notes/Equations
240
Measurement Expressions
The rms() function calculates the root mean square value. If the data's inner independent
is freq, and if frequency equals 0 (DC), then the function returns mag() rather than rms
value.
round()
Rounds to the nearest integer
Syntax
y = round(x)
Arguments
Name Description Default Range Type Required
x
number
None
(∞:∞)
real
Yes
Examples
a
a
a
a
a
a
=
=
=
=
=
=
round(0.1) returns 0
round(0.5) returns 1
round(0.9) returns 1
round(-0.1) returns 0
round(-0.5) returns -1
round(-0.9) returns -1
Defined in
Built in
See Also
int() (expmeas)
Note
The function name round() is used for more than one type of expression. For comparison, see the AEL
Function round() Function (ael). Also, for more information on the different expression types and the
contexts in which they are used, see Duplicated Expression Names (expmeas).
sgn()
Returns the integer sign of an integer or real number, as either 1 or -1
Syntax
y = sgn(x)
Arguments
Name Description Default Range Type
Required
x
Yes
number
None
(∞:∞)
Integer,
real
241
Measurement Expressions
Examples
a = sgn(-1) returns -1
a = sgn(1) returns 1
Defined in
Built in
See Also
abs() (expmeas), cint() (expmeas), exp() (expmeas), float() (expmeas), int() (expmeas),
log10() (expmeas), pow() (expmeas), sqrt() (expmeas)
Note
The function name sgn() is used for more than one type of expression. For comparison, see the Simulator
Expression sgn() Expression (expsim) and the AEL Function sgn() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
sin()
Returns the sine
Syntax
y = sin(x)
Arguments
Name Description
x
Default Range Type
number in radians None
(∞:∞)
Required
Integer, real, complex Yes
Examples
y = sin(pi/2) returns 1
Defined in
Built in
See Also
cos() (expmeas), tan() (expmeas)
242
Measurement Expressions
Note
The function name sin() is used for more than one type of expression. For comparison, see the Simulator
Expression sin() Expression (expsim) and the AEL Function sin() Function (ael). Also, for more information
on the different expression types and the contexts in which they are used, see Duplicated Expression
Names (expmeas).
sinc()
Returns the sinc of a number.
Syntax
y = sinc(x)
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
Integer, real, complex Yes
Examples
a = sinc(0.5) returns 0.959
Defined in
Built in
See Also
sin() (expmeas)
Notes/Equations
The sinc function is defined as sinc(x) = sin(pi*x)/ (pi*x) and sinc(0)=1.
Note
The function name sinc() is used for more than one type of expression. For comparison, see the Simulator
Expression sinc() Expression (expsim) and the AEL Function sinc() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
sinh()
Returns the hyperbolic sine
Syntax
y = sinh(x)
243
Measurement Expressions
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
Integer, real, complex Yes
Examples
a = sinh(0) returns 0
a = sinh(1) returns 1.1752
Defined in
Built in
See Also
cosh() (expmeas), tanh() (expmeas)
Note
The function name sinh() is used for more than one type of expression. For comparison, see the Simulator
Expression sinh() Expression (expsim) and the AEL Function sinh() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
sqr()
Returns the square of a number
Syntax
y = sqr(x)
Arguments
Name Description
Default Range Type
x
None
number to
square
(∞:∞)
Required
Integer, real, complex Yes
Examples
y = sqr(2) returns 4
Defined In
$HPEESOF_DIR/expressions/ael/elementary_fun.ael
sqrt()
Returns the square root of number
Syntax
244
Measurement Expressions
y = sqrt(x)
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
Integer, real, complex Yes
Examples
a = sqrt(4) returns 2
a = sqrt(2+j*1) returns 1.455+j*0.344
Defined in
Built in
See Also
abs() (expmeas), cint() (expmeas), exp() (expmeas), float() (expmeas), int() (expmeas),
log10() (expmeas), pow() (expmeas), sgn() (expmeas)
Note
The function name sqrt() is used for more than one type of expression. For comparison, see the Simulator
Expression sqrt() Expression (expsim) and the AEL Function sqrt() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
step()
Returns 0, 0.5, or 1
Syntax
y= step(x)
Arguments
Name Description Default Range Type
x
number
None
(∞:∞)
Required
Integer, real, complex Yes
Examples
a = step(-1.5) returns 0.000
a = step(0) returns 0.500
a = step(1.5) returns 1.000
Defined in
Built in
245
Measurement Expressions
Note
The function name step() is used for more than one type of expression. For comparison, see the Simulator
Expression step() Expression (expsim) and the AEL Function step() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
sum()
Returns the sum
Syntax
y = sum(x)
Arguments
Name Description
Default Range Type
Required
x
None
Yes
data to find
sum
(∞:∞)
Integer, real or
complex
Examples
a = sum([1, 2, 3]) returns 6
Defined in
Built in
See Also
max() (expmeas), mean() (expmeas), min() (expmeas)
Note
The function name sum() is used for more than one type of expression. For comparison, see the
Measurement Expression sum() Measurement (expmeas). Also, for more information on the different
expression types and the contexts in which they are used, see Duplicated Expression Names (expmeas).
tan()
Returns the tangent
Syntax
y = tan(x)
Arguments
Name Description
x
Default Range Type
number in radians None
(∞:∞)
Required
Integer, real, complex Yes
Examples
246
Measurement Expressions
a = tan(pi/4) returns 1
a = tan(+/-pi/2) returns +/- 1.633E16
Defined in
Built in
See Also
cos() (expmeas), sin() (expmeas)
Note
The function name tan() is used for more than one type of expression. For comparison, see the Simulator
Expression tan() Expression (expsim) and the AEL Function tan() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
tanh()
Returns the hyperbolic tangent
Syntax
y = tanh(x)
Arguments
Name Description
x
Default Range Type
number in radians None
(∞:∞)
Required
Integer, Real, complex Yes
Examples
a = tanh(0) returns 0
a = tanh(1) returns 0.761594
a = tanh(-1) returns -0.761594
Defined in
Built in
See Also
cosh() (expmeas), sinh() (expmeas)
247
Measurement Expressions
Note
The function name tanh() is used for more than one type of expression. For comparison, see the Simulator
Expression tanh() Expression (expsim) and the AEL Function tanh() Function (ael). Also, for more
information on the different expression types and the contexts in which they are used, see Duplicated
Expression Names (expmeas).
transpose()
Returns the transpose of a matrix
Syntax
y = transpose(Matrix)
Arguments
Name Description
Default Range Type
Required
Matrix square matrix to find the
transpose
None
Yes
(∞:∞)
Integer, Real or
Complex
Examples
a={{1, 2}, {3, 4}}
b=transpose(a)
returns {{1, 3}, {2, 4}}
Defined in
Built in
See Also
diagonal() (expmeas), inverse() (expmeas)
wtodbm()
Converts Watts to dBm and returns a real or complex number
Syntax
dbmVal = wtodbm(Value)
Arguments
Name Description
Default Range Type
Value Value in
Watts
None
(∞:∞)
Required
Real, Complex Yes
Examples
wtodbm01_M=wtodbm(0.01) returns 10
wtodbm1_M=wtodbm(1) returns 30
wtodbmC_M=wtodbm(complex(10,2)) returns 40.094/1.225
248
Measurement Expressions
Defined in
$HPEESOF_DIR/expressions/ael/elementary_fun.ael
See Also
dbmtow() (expmeas)
Note
The function name wtodbm() is used for more than one type of expression. For comparison, see the
Simulator Expression wtodbm() Expression (expsim). Also, for more information on the different
expression types and the contexts in which they are used, see Duplicated Expression Names (expmeas).
xor()
Returns an integer that represents the exclusive OR between arguments
Syntax
yXor = xor(x, y)
Arguments
Name Description Default Range Type
Required
x
number
None
(∞:∞)
Integer Yes
y
number
None
(∞:∞)
Integer Yes
Examples
a = xor(16, 32) returns 48
Defined in
Built in
Note
The function name xor() is used for more than one type of expression. For comparison, see the AEL
Function xor() Function (ael). Also, for more information on the different expression types and the
contexts in which they are used, see Duplicated Expression Names (expmeas).
zeros()
Returns zeros matrix
Syntax
y = zeros(rows, columns)
Arguments
249
Measurement Expressions
Name
Description
Default Range Type
rows
number of rows †
None
[i:∞)
Integer Yes
None
[i:∞)
Integer Yes
columns number of columns
†
Required
† If only one argument is supplied, then a square matrix is returned. If two are supplied,
then a matrix of zeros with size rows X cols is returned.
Examples
a=zeros(2) returns {{0, 0}, {0, 0}}
b=(2, 3) returns {{0, 0, 0}, {0, 0, 0}}
Defined in
Built in
See Also
identity() (expmeas), ones() (expmeas)
250
Measurement Expressions
Signal Processing Functions
This section describes the signal processing functions in detail. The functions are listed in
alphabetical order.
add rf() (expmeas)
ber pi4dqpsk() (expmeas)
ber qpsk() (expmeas)
eye() (expmeas)
eye amplitude() (expmeas)
eye closure() (expmeas)
eye fall time() (expmeas)
eye height() (expmeas)
eye rise time() (expmeas)
spec power() (expmeas)
add_rf()
Returns the sum of two Timed Complex Envelope signals defined by the triplet in-phase
(real or I(t)) and quadrature-phase (imaginary or Q(t)) part of a modulated carrier
frequency(Fc).
Syntax
y = add_rf(T1, T2)
Arguments
Name Description
Default Range Type
Required
T1
Timed Complex Envelope signals at carrier frequencies Fc1 None
(∞:∞)
Complex Yes
T2
Timed Complex Envelope signals at carrier frequencies Fc2 None
(∞:∞)
Complex Yes
Examples
y= add_rf(T1, T2)
Defined in
$HPEESOF_DIR/expressions/ael/signal_proc_fun.ael
Notes/Equations
Used in Signal processing designs that output Timed Signals using Timed Sinks
This equation determines the sum of two Timed Complex Envelope at a new carrier
frequency Fc3. Given Fc1 and Fc2 as the carrier frequencies of the two input waveforms,
the output carrier frequency Fc3 will be the greater of the two.
ber_pi4dqpsk()
Returns the symbol probability of error versus signal-to-noise ratio per bit for pi/4 DQPSK
modulation.
251
Measurement Expressions
Syntax
data = ber_pi4dqpsk(vIn, vOut, symRate, noise, samplingDelay, rotation, tranDelay,
pathDelay)
Arguments
Name
Description
Default
Range Type
Required
vIn
complex envelope voltage signals at the input node
None
(∞:∞)
Complex Yes
vOut
complex envelope voltage signals at the output node
None
(∞:∞)
Complex Yes
symRate
symbol rate (real) of the modulation signal
None
(0:∞)
Real
Yes
noise
RMS noise vector
None
(0:∞)
Real
Yes
samplingDelay clock phase in seconds
calculated [0:∞)
Real
Yes
rotation
carrier phase in radians
calculated [0:∞)
Real
Yes
tranDelay
time in seconds that causes this time duration of
symbols to be eliminated from the bit error rate
calculation †
calculated [0:∞)
Real
Yes
pathDelay
delay from input to output in seconds
calculated [0:∞)
Real
Yes
† Usually the filters in the simulation have transient responses, and the bit error rate
calculation should not start until these transient responses have finished.
Examples
y = ber_pi4dqpsk(videal[1], vout[1], 0.5e6, {0.1::-0.01::0.02})
Defined in
$HPEESOF_DIR/expressions/ael/digital_wireless_fun.ael
See Also
ber_qpsk() (expmeas), constellation() (expmeas)
Notes/Equations
Used in Circuit Envelope and Signal Processing simulations.
The arguments vIn and vOut usually come from a circuit envelope simulation, while noise
usually comes from a harmonic balance simulation, and is assumed to be additive white
Gaussian. It can take a scalar or vector value. The function uses the quasi-analytic
approach for estimating BER: for each symbol, Eb / N0 and BER are calculated
analytically; then the overall BER is the average of the BER values for the symbols.
Note that ber_pi4dqpsk returns a list of data:
data[0]= symbol probability of error versus Eb / N0
data[1]= path delay in seconds
data[2]= carrier phase in radians
252
data[3]= clock phase in seconds
data[4]= complex(Isample, Qsample)
Measurement Expressions
ber_qpsk()
Returns the symbol probability of error versus signal-to-noise ratio per bit for QPSK
modulation
Syntax
data = ber_qpsk(vIn, vOut, symRate, noise{, samplingDelay, rotation, tranDelay,
pathDelay})
Arguments
Name
Description
Default
Range Type
Required
vIn
complex envelope voltage signals at the input node
None
(∞:∞)
Complex Yes
vOut
complex envelope voltage signals at the output node
None
(∞:∞)
Complex Yes
symRate
symbol rate (real) of the modulation signal
None
(0:∞)
Real
Yes
noise
RMS noise vector
None
(0:∞)
Real
Yes
samplingDelay clock phase in seconds
calculated [0:∞)
Real
Yes
rotation
carrier phase in radians
calculated [0:∞)
Real
Yes
tranDelay
time in seconds that causes this time duration of
symbols to be eliminated from the bit error rate
calculation †
calculated [0:∞)
Real
Yes
pathDelay
delay from input to output in seconds
calculated [0:∞)
Real
Yes
† Usually the filters in the simulation have transient responses, and the bit error rate
calculation should not start until these transient responses have finished.
Examples
y = ber_qpsk(videal[1], vout[1], 1e6, {0.15::-0.01::0.04})
Defined in
$HPEESOF_DIR/expressions/ael/digital_wireless_fun.ael
See Also
ber_pi4dqpsk() (expmeas), constellation() (expmeas)
Notes/Equations
Used in Circuit Envelope and Signal Processing simulations.
The arguments vIn and vOut usually come from a circuit envelope simulation, while noise
usually comes from a harmonic balance simulation, and is assumed to be additive white
Gaussian. It can take a scalar or vector value. The function uses the quasi-analytic
253
Measurement Expressions
approach for estimating BER: for each symbol, Eb / N0 and BER are calculated
analytically; then the overall BER is the average of the BER values for the symbols.
Note that ber_qpsk returns a list of data:
data[0]= symbol probability of error versus Eb / N0
data[1]= path delay in seconds
data[2]= carrier phase in radians
data[3]= clock phase in seconds
data[4]= complex(Isample, Qsample)
eye()
Creates data for an eye diagram plot
Syntax
y = eye(data, symbolRate, Cycles, Delay)
Arguments
Name
Description
Default Range Type
Required
data
either numeric data or a time domain waveform typically
from the I or Q data channel
None
(∞:∞)
Complex
Yes
symbolRate symbol rate of the channel. For numeric data, the symbol None
rate is the reciprocal of the number of points in one cycle;
for a waveform, it is the frequency
(0:∞)
Real
Yes
Cycles
number of cycles to repeat
1
[1:∞)
Integer
No
Delay
sampling delay
0
[0:∞)
Integer,
Real
No
Examples
y = eye(I_data, symbol_rate)
Defined in
Built in
See Also
constellation() (expmeas), eye_amplitude() (expmeas), eye_closure() (expmeas),
eye_fall_time() (expmeas), eye_height() (expmeas), eye_rise_time() (expmeas)
eye_amplitude()
Returns eye amplitude
Syntax
y = eye_amplitude(Vout_time, Delay, BitRate, SamplePoint, WindowPct)
Arguments
254
Measurement Expressions
Name
Description
Default Range Type
Vout_time
time domain voltage waveform
None
(∞:∞)
Complex Yes
Delay
used to remove initial transient in the eye diagram and is
expressed in time units
None
[0:∞)
Real
Yes
BitRate
bit rate of the channel and is expressed in frequency units
None
[0:∞)
Real
Yes
SamplePoint marker name placed on the eye diagram measurement.
None
The independent value of this marker is used to determine
the symbol offset.
None
string
Yes
WindowPct
[0:1]
Real
Yes
used to determine level '1' and level '0' of the time domain None
waveform and its typical value is 0.2.
Required
Examples
Eye_amp = eye_amplitude(vout,12 ps,10 GHz, m1, 0.2)
Defined in
$HPEESOF_DIR/expressions/ael/DesignGuide_fun.ael
See Also
cross_hist() (expmeas), eye() (expmeas), eye_closure() (expmeas), eye_fall_time()
(expmeas), eye_height() (expmeas), eye_rise_time() (expmeas)
Notes/Equations
The eye_amplitude() function essentially takes the vertical histogram of the eye voltages
and subtracts the "0" level mean from "1" level mean within a given measurement
window.
eye_closure()
Returns eye closure
Syntax
y = eye_closure(Vout_time, Delay, BitRate, SamplePoint, WindowPct)
Arguments
255
Measurement Expressions
Name
Description
Default Range Type
Vout_time
time domain voltage waveform
None
(∞:∞)
Complex Yes
Delay
used to remove initial transient in the eye diagram and is
expressed in time units
None
[0:∞)
Real
Yes
BitRate
bit rate of the channel and is expressed in frequency units
None
[0:∞)
Real
Yes
SamplePoint marker name placed on the eye diagram measurement.
None
The independent value of this marker is used to determine
the symbol offset.
None
string
Yes
WindowPct
[0:1]
Real
Yes
used to determine level '1' and level '0' of the time domain None
waveform and its typical value is 0.2.
Required
Examples
Eye_Close = eye_closure(vout,12 ps,10 GHz, m1, 0.2)
Defined in
$HPEESOF_DIR/expressions/ael/DesignGuide_fun.ael
See Also
cross_hist() (expmeas), eye() (expmeas), eye_amplitude() (expmeas), eye_fall_time()
(expmeas), eye_height() (expmeas), eye_rise_time() (expmeas)
Notes/Equations
Computes the ratio of eye height to eye amplitude to provide eye closure.
eye_fall_time()
Returns eye fall time
Syntax
y = eye_fall_time(Vout_time,Delay,BitRate,SamplePoint,WindowPct)
Arguments
Name
Description
Default Range Type
Required
Vout_time
time domain voltage waveform
None
(∞:∞)
Complex Yes
Delay
used to remove initial transient in the eye diagram and is
expressed in time units
None
[0:∞)
Real
Yes
BitRate
bit rate of the channel and is expressed in frequency units
None
[0:∞)
Real
Yes
SamplePoint marker name placed on the eye diagram measurement.
None
The independent value of this marker is used to determine
the symbol offset.
None
string
Yes
WindowPct
[0:1]
Real
Yes
used to determine level '1' and level '0' of the time domain None
waveform and its typical value is 0.2.
256
Measurement Expressions
Examples
Eye_Fall = eye_fall_time(vout,12 ps,10 GHz, m1, 0.2)
Defined in
$HPEESOF_DIR/expressions/ael/DesignGuide_fun.ael
See Also
cross_hist() (expmeas), eye() (expmeas), eye_amplitude() (expmeas), eye_closure()
(expmeas), eye_height() (expmeas), eye_rise_time() (expmeas)
Notes/Equations
Computes 20% - 80% fall time of a time domain waveform.
eye_height()
Returns eye height
Syntax
y = eye_height(Vout_time, Delay, BitRate, SamplePoint, WindowPct)
Arguments
Name
Description
Default Range Type
Vout_time
time domain voltage waveform
None
(∞:∞)
Complex Yes
Delay
used to remove initial transient in the eye diagram and is
expressed in time units
None
[0:∞)
Real
Yes
BitRate
bit rate of the channel and is expressed in frequency units
None
[0:∞)
Real
Yes
SamplePoint marker name placed on the eye diagram measurement.
None
The independent value of this marker is used to determine
the symbol offset.
None
string
Yes
WindowPct
[0:1]
Real
Yes
used to determine level '1' and level '0' of the time domain None
waveform and its typical value is 0.2.
Examples
Eye_Ht = eye_height(vout,12 ps,10 GHz, m1, 0.2)
Defined in
$HPEESOF_DIR/expressions/ael/DesignGuide_fun.ael
See Also
257
Required
Measurement Expressions
cross_hist() (expmeas), eye() (expmeas), eye_amplitude() (expmeas), eye_closure()
(expmeas), eye_fall_time() (expmeas), eye_rise_time() (expmeas)
Notes/Equations
The eye_height() function essentially takes the vertical histogram of the eye voltages and
computes inner bounds of the eye opening.
eye_rise_time()
Returns eye rise time
Syntax
y = eye_rise_time(Vout_time,Delay,BitRate,SamplePoint,WindowPct)
Arguments
Name
Description
Default Range Type
Vout_time
time domain voltage waveform
None
(∞:∞)
Complex Yes
Delay
used to remove initial transient in the eye diagram and is
expressed in time units
None
[0:∞)
Real
Yes
BitRate
bit rate of the channel and is expressed in frequency units
None
[0:∞)
Real
Yes
SamplePoint marker name placed on the eye diagram measurement.
None
The independent value of this marker is used to determine
the symbol offset.
None
string
Yes
WindowPct
[0:1]
Real
Yes
used to determine level '1' and level '0' of the time domain None
waveform and its typical value is 0.2.
Required
Examples
Eye_Rise = eye_rise_time(vout,12 ps,10 GHz, m1, 0.2)
Defined in
$HPEESOF_DIR/expressions/ael/DesignGuide_fun.ael
See Also
cross_hist() (expmeas), eye() (expmeas), eye_amplitude() (expmeas), eye_closure()
(expmeas), eye_fall_time() (expmeas), eye_height() (expmeas)
Notes/Equations
Computes 20% - 80% rise time of a time domain waveform.
spec_power()
258
Measurement Expressions
Returns the integrated signal power (dBm) of a spectrum
Syntax
y = spec_power(spectralData{, lowerFrequencyLimit, upperFrequencyLimit})
Arguments
Name
Description
Default
Range
Type Required
spectralData
spectral data in
dBm
None
None
Real Yes
lowerFrequencyLimit lower frequency
min(indep(spectralData)) (-∞:∞)
limit to be used in
calculating the
integrated power
Real No
upperFrequencyLimit upper frequency
max(indep(spectralData)) [lowerFrequencyLimit:∞) Real No
limit to be used in
calculating the
integrated power
Examples
total_power = spec_power(dBm(Mod_Spectrum), 60 MHz, 71 MHz)
where Mod_Spectrum is the instance name of a SpectrumAnalyzer sink component,
will return the integrated power between 60 and 71 MHz.
total_power = spec_power(dBm(fs(Vout[1])), indep(m1), indep(m2))
where Vout is a named node in a Circuit Envelope simulation, will return the
integrated power between markers 1 and 2.
Defined in
$HPEESOF_DIR/expressions/ael/signal_proc_fun.ael
Notes/Equations
Used in Circuit Envelope and Signal Processing simulations.
This expression can be used with spectral data of up to 4 dimensions (frequency should be
the inner dimension).
The spec_power() function returns the power (in dBm) of a spectrum integrated between
the lower and upper frequency limits specified. If no lower (upper) limit is specified, the
lowest (highest) frequency in the spectral data is used instead.
The input spectral data must be in dBm. Spectral data can be generated in several
different ways, such as applying the fs() expression on voltage or current time domain
data or using the SpectrumAnalyzer sink component.
The fs() expression returns the voltage or current spectrum of the input data and so the
dBm() expression should be applied to the fs() output before it is passed to the
spec_power() expression. The frequency axis values in the spectral data returned by fs()
are in Hz and so if lower and/or upper frequency limits are to be passed to spec_power(),
they should be specified in Hz.
259
Measurement Expressions
Similarly, the SpectrumAnalyzer sink component returns the voltage spectrum of the input
signal and so the dBm() expression should be applied to the spectral data generated by
SpectrumAnalyzer before it is passed to the spec_power() expression. The frequency axis
values in the spectral data generated by SpectrumAnalyzer are in Hz, so if lower and/or
upper frequency limits are to be passed to spec_power(), they should be specified in Hz.
260
Measurement Expressions
S-Parameter Analysis Functions for Measurement
Expressions
This section describes the S-parameter analysis functions in detail. The functions are listed
in alphabetical order.
abcdtoh() (expmeas)
abcdtos() (expmeas)
abcdtoy() (expmeas)
abcdtoz() (expmeas)
bandwidth func() (expmeas)
center freq() (expmeas)
dev lin gain() (expmeas)
dev lin phase() (expmeas)
ga circle() (expmeas)
gain comp() (expmeas)
gl circle() (expmeas)
gp circle() (expmeas)
gs circle() (expmeas)
htoabcd() (expmeas)
htos() (expmeas)
htoy() (expmeas)
htoz() (expmeas)
ispec() (expmeas)
l stab circle() (expmeas)
l stab circle center radius() (expmeas)
l stab region() (expmeas)
map1 circle() (expmeas)
map2 circle() (expmeas)
max gain() (expmeas)
mu() (expmeas)
mu prime() (expmeas)
ns circle() (expmeas)
ns pwr int() (expmeas)
ns pwr ref bw() (expmeas)
phase comp() (expmeas)
pwr gain() (expmeas)
ripple() Measurement (expmeas)
sm gamma1() (expmeas)
sm gamma2() (expmeas)
sm y1() (expmeas)
sm y2() (expmeas)
sm z1() (expmeas)
sm z2() (expmeas)
s stab circle() (expmeas)
s stab circle center radius() (expmeas)
s stab region() (expmeas)
stab fact() (expmeas)
stab meas() (expmeas)
stoabcd() (expmeas)
stoh() (expmeas)
stos() (expmeas)
261
stot() (expmeas)
stoy() (expmeas)
stoz() (expmeas)
tdr_step_impedance() (expmeas)
tdr sp gamma() (expmeas)
tdr sp imped() (expmeas)
tdr step imped() (expmeas)
ttos() (expmeas)
unilateral figure() (expmeas)
unwrap() (expmeas)
v dc() (expmeas)
volt gain() (expmeas)
volt gain max() (expmeas)
vswr() (expmeas)
write snp() (expmeas)
yin() (expmeas)
yopt() (expmeas)
ytoabcd() (expmeas)
ytoh() (expmeas)
ytos() (expmeas)
ytoz() (expmeas)
zin() (expmeas)
zopt() (expmeas)
ztoabcd() (expmeas)
ztoh() (expmeas)
ztos() (expmeas)
ztoy() (expmeas)
Measurement Expressions
abcdtoh()
This measurement transforms the chain (ABCD) matrix of a 2-port network to a hybrid
matrix.
Syntax
h=abcdtoh(a)
Arguments
Name Description
Default Range Type
A
None
chain (ABCD) matrix of a 2-port
network
(∞:∞)
Examples
h=abcdtoh(a)
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
See Also
262
Required
Complex Yes
Measurement Expressions
abcdtos() (expmeas), abcdtoy() (expmeas), abcdtoz() (expmeas), htoabcd() (expmeas),
stoabcd() (expmeas), ytoabcd() (expmeas), ztoabcd() (expmeas)
abcdtos()
This measurement transforms the chain (ABCD) matrix of a 2-port network to a scattering
matrix.
Syntax
sp = abcdtos(A, zRef)
Arguments
Name Description
Default Range Type
Required
A
chain (ABCD) matrix of a 2-port
network
None
(∞:∞)
Complex
Yes
zRef
reference impedance
50.0
(∞:∞)
Integer, real or
complex
No
Examples
sp = abcdtos(a, 50)
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
See Also
abcdtoh() (expmeas), abcdtoy() (expmeas), abcdtoz() (expmeas), htoabcd() (expmeas),
stoabcd() (expmeas), ytoabcd() (expmeas), ztoabcd() (expmeas)
abcdtoy()
This measurement transforms the chain (ABCD) matrix of a 2-port network to an
admittance matrix.
Syntax
y = abcdtoy(a)
Arguments
Name Description
Default Range Type
A
None
chain (ABCD) matrix of a 2-port
network
(∞:∞)
Examples
y = abcdtoy(a)
Defined in
263
Required
Complex Yes
Measurement Expressions
$HPEESOF_DIR/expressions/ael/network_fun.ael
See Also
abcdtoh() (expmeas), abcdtos() (expmeas), abcdtoz() (expmeas), htoabcd() (expmeas),
stoabcd() (expmeas), ytoabcd() (expmeas), ztoabcd() (expmeas)
abcdtoz()
This measurement transforms the chain (ABCD) matrix of a 2-port network to impedance
matrix.
Syntax
z = abcdtoz(a)
Arguments
Name Description
Default Range Type
A
None
chain (ABCD) matrix of a 2-port
network
(∞:∞)
Required
Complex Yes
Examples
z = abcdtoz(a)
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
See Also
abcdtoh() (expmeas), abcdtos() (expmeas), abcdtoy() (expmeas), htoabcd() (expmeas),
stoabcd() (expmeas), ytoabcd() (expmeas), ztoabcd() (expmeas)
bandwidth_func()
Returns the bandwidth at the specified level as a real number. Typically used in filter
application to calculate the 1, 3 dB bandwidth.
Syntax
bw = bandwidth_func(Data, DesiredValue, Type)
Arguments
264
Measurement Expressions
Name
Description
Default Range Type
Required
Data
data (usually gain) to find the bandwidth
None
(∞:∞)
Integer,
Real
Yes
DesiredValue A single value representing the desired bandwidth
level.
None
(∞:∞)
Real
Yes
Type
0
[0:3] † Integer
†
0
1
2
3
Type of response
No
Type:
- Band-pass
- Band-stop
- Low-pass
- High-pass
Examples
We assume that a S-Parameter analysis has been performed.
bw3dB = bandwidth_func(db(S21), 3) returns the 3dB bandwidth
Defined in
$HPEESOF_DIR/expressions/ael/rf_system_fun.ael
See Also
center_freq() (expmeas)
Notes/Equations
This function returns the bandwidth of a filter response. Bandwidth is defined as the
difference between the upper and lower frequency at which the amplitude response is
DesiredValue dB below the maximum amplitude. It uses an iterative process to find the
bandwidth on non-ideal responses for the band limited responses.
Data can be from 1 to 4 dimensions.
center_freq()
Returns the center frequency at the specified level as a real number.
Typically used in filter application to calculate the center frequency at 1, 3 dB bandwidth.
Syntax
fc = center_freq(Data, ReferenceBW)
Arguments
Name
Description
Default Range Type
Data
data (usually gain) to find the center frequency
None
(∞:∞)
Complex Yes
ReferenceBW a single value representing the reference bandwidth None
(∞:∞)
Real
265
Required
Yes
Measurement Expressions
Examples
We assume that a S-Parameter analysis has been performed.
fc3 = center_freq(db(S21), 3) returns the center frequency using the 3dB point
as reference
Defined in
$HPEESOF_DIR/expressions/ael/rf_system_fun.ael
See Also
bandwidth_func() (expmeas)
Notes/Equations
This function returns the center frequency of a filter response. Linear interpolation is
performed between data points. The function uses an iterative process to find the
bandwidth on non-ideal responses. The data can be from 1 to 4 dimensions.
dev_lin_gain()
Given a variable sweep over a frequency range, a linear least-squares fit is performed on
the gain of the variable, and the deviation from this linear fit is calculated at each
frequency point.
Syntax
y = dev_lin_gain(voltGain)
Arguments
Name
Description
Default Range Type
voltGain gain as a function of frequency None
[0:∞)
Required
Complex Yes
Examples
a = dev_lin_gain(volt_gain(S,PortZ(1),PortZ(2)))
Defined in
$HPEESOF_DIR/expressions/ael/rf_system_fun.ael
See Also
dev_lin_phase() (expmeas), diff() (expmeas), phasedeg() (ael), phaserad() (ael),
pwr_gain() (expmeas), ripple() (expmeas), unwrap() (expmeas), volt_gain() (expmeas)
266
Measurement Expressions
dev_lin_phase()
Given a variable sweep over a frequency range, a linear least-squares fit is performed on
the phase of the variable, and the deviation from this linear fit is calculated at each
frequency point.
Syntax
y = dev_lin_phase(voltGain)
Arguments
Name
Description
voltGain function of
frequency
Default Range Type
None
[0:∞)
Required
Complex Yes
Examples
a = dev_lin_phase(S21)
Defined in
$HPEESOF_DIR/expressions/ael/rf_system_fun.ael
See Also
dev_lin_gain() (expmeas), diff() (expmeas), phasedeg() (expmeas), phaserad()
(expmeas), pwr_gain() (expmeas), ripple() (expmeas), unwrap() (expmeas), volt_gain()
(expmeas)
Notes/Equations
In order to use this function, the Group Delay option must be enabled in the S-parameter
analysis setup. For more information, refer to " Calculating Group Delay " in your " SParameter Simulation " documentation.
ga_circle()
Generates an available gain circle.
Syntax
y = ga_circle(S, gain, numOfPts, numCircles, gainStep)
Arguments
267
Measurement Expressions
Name
Description
Default Range Type
Required
S
scattering matrix of a 2-port network.
None
(∞:∞)
Complex
Yes
gain
specified gain in dB
†
[0:∞)
Integer or Real
array
No
numOfPts
desired number of points per circle
51
[1:∞)
Integer
No
numCircles number of desired circles. This is used if gain is
not specified.
None
[0:∞)
Integer
No
gainStep
1.0
[0:∞)
Integer or Real
No
gain step size. This is used if gain is not specified.
† Default value for gain is min(max_gain(S)) - {1, 2, 3}
Examples
circleData = ga_circle(S, 2, 51)
circleData = ga_circle(S, {2, 3, 4}, 51) return the points on the circle(s).
circleData = ga_circle(S, , 51, 5, 0.5) return the points on the circle(s) for
5 circles at maxGain - {0,0.5,1.0,1.5,2.0}
circleData = ga_circle(S, , , 2, 1.0) return the points on the circle(s) for 2
circles at maxGain - {0,1.0}
Defined in
$HPEESOF_DIR/expressions/ael/circle_fun.ael
See Also
gl_circle() (expmeas), gp_circle() (expmeas), gs_circle() (expmeas)
Notes/Equations
This function is used in Small-signal S-parameter simulations.
The function generates the constant available-gain circle resulting from a source
mismatch. The circle is defined by the loci of the source-reflection coefficients resulting in
the specified gain.
A gain circle is created for each value of the swept variable(s). Multiple gain values can be
specified for a scattering parameter that has dimension less than four. This measurement
is supported for 2-port networks only.
If gain and numCircles are not specified, gain circles are drawn at min(max_gain(S)) {0,1,2,3}. That is, gain is calculated at a loss of 0,1,2,3 dB from maxGain.
If gain is not specified and numCircles is given, then numCircles gain circles are drawn at
gainStep below max_gain(). Gain is also limited by max_gain(S). That is, if gain >
max_gain(S), then the circle is generated at max_gain(S).
268
Measurement Expressions
Where:
gain_comp()
Returns gain compression
Syntax
y = gain_comp(Sji)
Arguments
Name Description
Default Range Type
Sji
None
Sji is a power-dependent complex transmission coefficient
obtained from large-signal S-parameter simulation.
(∞:∞)
Required
Complex Yes
Examples
gc = gain_comp(S21[::, 0])
Defined in
$HPEESOF_DIR/expressions/ael/rf_system_fun.ael
See Also
phase_comp() (expmeas)
Notes/Equations
Used in Large-signal S-parameter simulations.
This measurement calculates the small-signal minus the large-signal power gain, in dB.
The first power point (assumed to be small) is used to calculate the small-signal power
gain.
gl_circle()
Returns a load-mismatch gain circle.
Syntax
y = gl_circle(S, gain, numOfPts, numCircles, gainStep)
269
Measurement Expressions
Arguments
Name
Description
Default
Range Type
Required
S
scattering matrix of a 2-port network.
None
(∞:∞)
Complex
Yes
gain
specified gain in dB
maxGain - {0, 1,
2, 3} †
[0:∞)
Integer or Real No
array
numOfPts
desired number of points per circle
51
[1:∞)
Integer
No
numCircles number of desired circles. This is used if
gain is not specified.
None
[0:∞)
Integer
No
gainStep
1.0
[0:∞)
Integer or Real No
gain step size. This is used if gain is not
specified.
† Where maxGain = 10*log(1 / (1 - mag(S22)**2))
Examples
circleData = gl_circle(S, 2, 51)
circleData = gl_circle(S, {2, 3, 4}, 51) return the points on the circle(s).
circleData = gl_circle(S, , 51, 5, 0.5) return the points on the circle(s) for
5 circles at maxGain - {0,0.5,1.0,1.5,2.0}
circleData = gl_circle(S, , , 2, 1.0) return the points on the circle(s) for 2
circles at maxGain - {0,1.0}
Defined in
$HPEESOF_DIR/expressions/ael/circle_fun.ael
See Also
ga_circle() (expmeas), gp_circle() (expmeas), gs_circle() (expmeas)
Notes/Equations
Used in Small-signal S-parameter simulations.
This function generates the unilateral gain circle resulting from a load mismatch. The circle
is defined by the loci of the load-reflection coefficients that result in the specified gain.
A gain circle is created for each value of the swept variable(s). Multiple gain values can be
specified for a scattering parameter that has dimension less than four. This measurement
is supported for 2-port networks only.
If gain and numCircles are not specified, gain circles are drawn at maxGain - {0,1,2,3}.
That is, gain is calculated at a loss of 0,1,2,3 dB from the maximum gain. If gain is not
specified and numCircles is given, then numCircles gain circles are drawn at gainStep
below maxGain. Gain is also limited by maxGain. That is, if gain > maxGain, then the
circle is generated at maxGain.
270
Measurement Expressions
Where Gabs is the absolute gain, and is given by:
gp_circle()
Generates a power gain circle.
Syntax
y = gp_circle(S, gain, numOfPts, numCircles, gainStep)
Arguments
Name
Description
Default Range Type
Required
S
scattering matrix of a 2-port network.
None
(∞:∞)
Complex
Yes
gain
specified gain in dB
†
[0:∞)
Integer or Real
array
No
numOfPts
desired number of points per circle
51
[1:∞)
Integer
No
numCircles number of desired circles. This is used if gain is
not specified.
None
[0:∞)
Integer
No
gainStep
1.0
[0:∞)
Integer or Real
No
gain step size. This is used if gain is not specified.
† Default value for gain is min(max_gain(S)) - {1, 2, 3}
Examples
circleData = gp_circle(S, 2, 51)
circleData = gp_circle(S, {2, 3, 4}, 51) return the points on the circle(s).
circleData = gp_circle(S, , 51, 5, 0.5) return the points on the circle(s) for
5 circles at maxGain - {0,0.5,1.0,1.5,2.0}
circleData = gp_circle(S, , , 2, 1.0) return the points on the circle(s) for 2
circles at maxGain - {0,1.0}
Defined in
$HPEESOF_DIR/expressions/ael/circle_fun.ael
See Also
ga_circle() (expmeas), gl_circle() (expmeas), gs_circle() (expmeas)
271
Measurement Expressions
Notes/Equations
Used in Small-signal S-parameter simulations.
This function generates a constant-power-gain circle resulting from a load mismatch. The
circle is defined by the loci of the output-reflection coefficients that result in the specified
gain.
A gain circle is created for each value of the swept variable(s). Multiple gain values can be
specified for a scattering parameter that has dimension less than four. This measurement
is supported for 2-port networks only.
If gain and numCircles are not specified, gain circles are drawn at min(max_gain(S)) {0,1,2,3}. That is, gains are calculated at a loss of 0,1,2,3 dB from the maximum gain. If
gain is not specified and numCircles is given, then numCircles gain circles are drawn at
gainStep below max_gain(). Gain is also limited by max_gain(S). That is, if gain >
max_gain(S), then the circle is generated at max_gain(S)).
Where:
gs_circle()
Returns a source-mismatch gain circle.
Syntax
y = gs_circle(S, gain, numOfPts, numCircles, gainStep)
Arguments
Name
Description
Default
Range Type
Required
S
scattering matrix of a 2-port network.
None
(∞:∞)
Complex
Yes
gain
specified gain in dB
maxGain - {0, 1,
2, 3} †
[0:∞)
Integer or Real No
array
numOfPts
desired number of points per circle
51
[1:∞)
Integer
No
numCircles number of desired circles. This is used if
gain is not specified.
None
[0:∞)
Integer
No
gainStep
1.0
[0:∞)
Integer or Real No
gain step size. This is used if gain is not
specified.
† Where maxGain = 10*log(1 / (1 - mag(S11)**2))
272
Measurement Expressions
Examples
circleData = gs_circle(S, 2, 51)
circleData = gs_circle(S, {2, 3, 4}, 51) return the points on the circle(s).
circleData = gs_circle(S, , 51, 5, 0.5) return the points on the circle(s) for
5 circles at maxGain - {0,0.5,1.0,1.5,2.0}
circleData = gs_circle(S, , , 2, 1.0) return the points on the circle(s) for 2
circles at maxGain - {0,1.0}
Defined in
$HPEESOF_DIR/expressions/ael/circle_fun.ael
See Also
ga_circle() (expmeas), gl_circle() (expmeas), gp_circle() (expmeas)
Notes/Equations
Used in Small-signal S-parameter simulations.
This function generates the unilateral gain circle resulting from a source mismatch. The
circle is defined by the loci of the source-reflection coefficients that result in the specified
gain. A gain circle is created for each value of the swept variable(s). Multiple gain values
can be specified for a scattering parameter that has dimension less than four. This
measurement is supported for 2-port networks only.
If gain and numCircles are not specified, gain circles are drawn at maxGain - {0,1,2,3}.
That is, gain values are calculated at a loss of 0,1,2,3 dB from the maximum gain. If gain
is not specified and if numCircles is given, then numCircles gain circles are drawn at
gainStep below maxGain. Gain is also limited by maxGain. That is, if gain > maxGain,
then the circle is generated at maxGain.
Where Gabs is the absolute gain, and is given by:
htoabcd()
This measurement transforms the hybrid matrix of a 2-port network to a chain (ABCD)
matrix.
Syntax
273
Measurement Expressions
a = htoabcd(H)
Arguments
Name Description
H
Default Range Type
hybrid matrix of a 2-port network None
(∞:∞)
Required
Complex Yes
Examples
a = htoabcd(H)
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
See Also
abcdtoh() (expmeas), htoz() (expmeas), ytoh() (expmeas)
htos()
This measurement transforms the hybrid matrix of a 2-port network to a scattering
matrix.
Syntax
sp = htos(h, zRef)
Arguments
Name Description
Default Range Type
Required
H
hybrid matrix of a 2-port network None
(∞:∞)
Complex
Yes
zRef
reference impedance
(∞:∞)
Integer, real or
complex
No
50.0
Examples
sp = htos(h, 50)
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
See Also
htoy() (expmeas), htoz() (expmeas), stoh() (expmeas)
htoy()
274
Measurement Expressions
This measurement transforms the hybrid matrix of a 2-port network to an admittance
matrix.
Syntax
y = htoy(H)
Arguments
Name Description
H
Default Range Type
hybrid matrix of a 2-port network None
(∞:∞)
Required
Complex Yes
Examples
y = htoy(H)
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
See Also
htos() (expmeas), htoz() (expmeas), ytoh() (expmeas)
htoz()
This measurement transforms the hybrid matrix of a 2-port network to an impedance
matrix.
Syntax
z = htoz(H)
Arguments
Name Description
H
Default Range Type
hybrid matrix of a 2-port network None
(∞:∞)
Required
Complex Yes
Examples
z = htoz(h)
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
See Also
htos() (expmeas), htoy() (expmeas), ytoh() (expmeas)
275
Measurement Expressions
ispec()
Returns the current frequency spectrum
Syntax
y = ispec(current)
Arguments
Name Description Default Range Type
current current
None
(∞:∞)
Required
Real, Complex Yes
Examples
a = ispec(i1)
Defined In
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
pspec() (expmeas), vspec() (expmeas)
Notes/Equations
This measurement gives a current frequency spectrum. The measurement gives a set of
RMS currents at each frequency.
l_stab_circle()
Returns load (output) stability circles.
Syntax
y = l_stab_circle(S, numOfPts)
Arguments
Name
Description
S
scattering matrix of a 2-port network. None
numOfPts desired number of points per circle
Default Range Type
51
Required
(∞:∞)
Complex Yes
[1:∞)
Integer
No
Examples
circleData = l_stab_circle(S, 51) returns the points on the circle(s).
276
Measurement Expressions
Defined in
$HPEESOF_DIR/expressions/ael/circle_fun.ael
See Also
l_stab_circle_center_radius() (expmeas), l_stab_region() (expmeas), s_stab_circle()
(expmeas), s_stab_region() (expmeas)
Notes/Equations
Used in Small-signal S-parameter simulations.
The function generates a load stability circle. The circle is defined by the loci of loadreflection coefficients where the magnitude of the source-reflection coefficient is 1.
A circle is created for each value of the swept variable(s). This measurement is supported
for 2-port networks only.
Use the function _l_stab_circle_center_radius()_ to find the center and radius of the
stability circle.
Use the function _l_stab_region(S)_ to determine the region of stability.
l_stab_circle_center_radius()
Returns the center and radius of the load (output) stability circle
Syntax
l_cr = l_stab_circle_center_radius(S, Type)
Arguments
Name Description
Default Range
Type
Required
S
2-port S-Parameters
None
None
Complex Yes
Type
Type of parameter to
return
"both"
["both","center","radius"] String
No
Examples
1. l_cr=l_stab_circle_center_radius(S) returns a 1X2 matrix containing center
and radius
lCirc=expand(circle(l_cr(1), real(l_cr(2)), 51)) returns data for the load
stability circle
2. l_radius=l_stab_circle_center_radius(S, "radius") returns the radius
Defined in
$HPEESOF_DIR/expressions/ael/circle_fun.ael
277
Measurement Expressions
See Also
l_stab_circle() (expmeas), s_stab_circle() (expmeas), s_stab_circle_center_radius()
(expmeas)
Notes/Equations
Used in Small-signal S-parameter simulations.
If the argument Type is not specified, the function returns complex data. Although radius
is of type real, the values are returned as complex. Therefore, when using the returned
radius, use the real part. To obtain the radius as a real number, set the Type argument to
radius .
l_stab_region()
This expression returns a string identifying the region of stability of the corresponding load
stability circle.
Syntax
y = l_stab_region(S)
Arguments
Name Description
S
Default Range Type
scattering matrix of a 2-port network. None
(∞:∞)
Required
Complex Yes
Examples
region = l_stab_region(S) returns "Outside" or "Inside".
Defined in
$HPEESOF_DIR/expressions/ael/circle_fun.ael
See Also
l_stab_circle() (expmeas), s_stab_circle() (expmeas), s_stab_region() (expmeas)
Notes/Equations
Used in Small-signal S-parameter simulations.
map1_circle()
Returns source-mapping circles from port 2 to port 1.
Syntax
circleData=map1_circle(S, numOfPts)
278
Measurement Expressions
Arguments
Name
Description
S
scattering matrix of a 2-port network. None
numOfPts desired number of points per circle
Default Range Type
51
Required
(∞:∞)
Complex Yes
[1:∞)
Integer
No
Examples
circleData=map1_circle(S, 51) returns the points on the circle(s).
Defined in
$HPEESOF_DIR/expressions/ael/circles_fun.ael
See Also
map2_circle() (expmeas)
Notes/Equations
Used in Small-signal S-parameter simulations
The function maps the set of terminations with unity magnitude at port 2 to port 1. The
circles are defined by the loci of terminations on one port as seen at the other port. A
source-mapping circle is created for each value of the swept variable(s). This
measurement is supported for 2-port networks only.
map2_circle()
Returns load-mapping circles from port 1 to port 2.
Syntax
circleData=map2_circle(S, numOfPts)
Arguments
Name
Description
S
scattering matrix of a 2-port network. None
numOfPts desired number of points per circle
Default Range Type
51
Required
(∞:∞)
Complex Yes
[1:∞)
Integer
No
Examples
circleData=map2_circle(S, 51) returns the points on the circle(s).
Defined in
$HPEESOF_DIR/expressions/ael/circle_fun.ael
279
Measurement Expressions
See Also
map1_circle() (expmeas)
Notes/Equations
Used in Small-signal S-parameter simulations
The function maps the set of terminations with unity magnitude at port 1 to port 2. The
circles are defined by the loci of terminations on one port as seen at the other port. A
source-mapping circle is created for each value of the swept variable(s). This
measurement is supported for 2-port networks only.
max_gain()
Given a 2 x 2 scattering matrix, this measurement returns the maximum available and
stable gain (in dB) between the input and the measurement ports.
Syntax
y = max_gain(S)
Arguments
Name Description
S
Default Range Type
scattering matrix of 2-port network None
(∞:∞)
Required
Complex Yes
Examples
y = max_gain(S)
Defined in
$HPEESOF_DIR/expressions/ael/rf_system_fun.ael
See Also
sm_gamma1() (expmeas), sm_gamma2() (expmeas), stab_fact() (expmeas),
stab_meas() (expmeas)
Notes/Equations
This function should be used in a stable system, i.e. when the stability factor (k) is greater
than 1. The function actually works for both k > 1 and k <= 1. If k > 1, then k is used in
the max gain calculations. However, if k <= 1, then k = 1 is used in the max gain
calculations.
280
mu()
Measurement Expressions
Returns the geometrically derived stability factor for the load.
Syntax
y = mu(S)
Arguments
Name Description
Default Range Type
S
None
scattering matrix of a 2-port
network
(∞:∞)
Required
Complex Yes
Examples
x=mu(S)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
mu_prime() (expmeas)
Notes/Equations
1. This measurement gives the distance from the center of the Smith chart to the
nearest output (load) stability circle. This stability factor is given by:
mu = {1-|S11 |2} / {|S22 - conj(S11 )*Delta | + |S12 *S21 | }
where Delta is the determinant of the S-parameter matrix. Having mu > 1 is the
single necessary and sufficient condition for unconditional stability of the 2-port
network.
2. The Mu component is available in the Simulation-S_Param palette.
Reference
1. M. L. Edwards and J. H. Sinsky, "A new criterion for linear 2-port stability using
geometrically derived parameters", IEEE Transactions on Microwave Theory and
Techniques, Vol. 40, No. 12, pp. 2303-2311, Dec. 1992.
mu_prime()
Returns the geometrically derived stability factor for the source.
Syntax
y = mu_prime(S)
281
Measurement Expressions
Arguments
Name Description
Default Range Type
S
None
scattering matrix of a 2-port
network
(∞:∞)
Required
Complex Yes
Examples
x=mu_prime(S)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
mu() (expmeas)
Notes/Equations
This measurement gives the distance from the center of the Smith chart to the nearest
unstable-input (source) stability circle. This stability factor is given by:
mu_prime = {1-|S22 |2} / {|S11 - conj(S 22 )*Delta | + |S21 *S12 | }
where Delta is the determinant of the S-parameter matrix. Having mu_prime > 1 is the
single necessary and sufficient condition for unconditional stability of the 2-port network.
Reference
M. L. Edwards and J. H. Sinsky, "A new criterion for linear 2-port stability using
geometrically derived parameters", IEEE Transactions on Microwave Theory and
Techniques, Vol. 40, No. 12, pp. 2303-2311, Dec. 1992.
ns_circle()
Returns noise-figure circles.
Syntax
y = ns_circle(nf2, NFmin, Sopt, rn, numOfPts, numCircles, NFStep)
Arguments
282
Measurement Expressions
Name
Description
Default Range Type
Required
nf2
specified noise figure
†
(∞:∞)
Real
No
NFmin
minimum noise figure
None
[0:∞)
Integer or
Real
Yes
Sopt
optimum mismatch
None
[0:∞)
Complex
Yes
rn
equivalent normalized noise resistance of a 2-port
network ††
None
[0:∞)
Complex
Yes
numOfPts
desired number of points per circle
51
[1:∞)
Integer
No
numCircles number of desired circles. This is used if nf2 is not
specified.
None
[0:∞)
Integer
No
NFStep
1.0
[0:∞)
Integer or
Real
No
nf step size. This is used if nf2 is not specified.
† If nf2 is NULL or not specified the default is max(NFmin)+{0,1,2,3}.
†† rn = Rn/zRef where Rn is the equivalent noise resistance and zRef is the reference
impedance.
Examples
circleData = ns_circle(0+NFmin, NFmin, Sopt, Rn/50, 51)
circleData = ns_circle(NULL, NFmin, Sopt,Rn/50,51) return the points on the
circle for 4 circles at max(NFmin)+{0,1,2,3}
Returns the points on the circle(s):
circleData = ns_circle({0, 1}+NFmin, NFmin, Sopt, Rn/50, 51)
Returns the points on the circle(s) for 3 circles at max(NFmin) + {0, 0.5,
1.0}:
circleData = ns_circle(, NFmin, Sopt, Rn/50, 51, 3, 0.5)
Returns the points on the circle(s) for 3 circles at max(NFmin) + {0, 1, 2.0}:
circleData = ns_circle(, NFmin, Sopt, Rn/50, , 3)
Defined in
$HPEESOF_DIR/expressions/ael/circle_fun.ael
Notes/Equations
Used in Small-signal S-parameter simulations and Harmonic Balance analysis.
The expression generates constant noise-figure circles. The circles are defined by the loci
of the source-reflection coefficients that result in the specified noise figure. NFmin, Sopt,
and Rn are generated from noise analysis.
A circle is created for each value of the swept variable(s).
If both nf2 and numCircles are specified, then circles are drawn at nf2 values (numCircles
is not used).
If nf2 and numCircles are not specified, then nf2 circles are drawn at max(NFmin) +
{0,1,2,3}.
If nf2 is not specified, and numCircles is given, then numCircles nf2 circles are drawn at
283
NFStep above max(NFmin).
Measurement Expressions
If nf2 is specified, and numCircles is not specified, then circles are drawn at nf2 values.
ns_pwr_int()
Returns the integrated noise power
Syntax
y = ns_pwr_int(Sji, nf, resBW, stop)
Arguments
Name Description
Default Range Type
Sji
complex transmission coefficient
None
(∞:∞)
Complex Yes
nf
noise figure at the output port (in dB)
None
(∞:∞)
Complex Yes
None
(∞:∞)
Complex Yes
stop value (works for nonuniform delta frequency) None
[0:∞)
Real
resBW user-defined resolution bandwidth
stop
Required
No
Examples
Y = ns_pwr_int(S21, nf2, 1MHz)
Defined in
$HPEESOF_DIR/expressions/ael/rf_system_fun.ael
See Also
ns_pwr_ref_bw() (expmeas), snr() (expmeas)
Notes/Equations
Used in Small-signal S-parameter simulation
This is the integrated noise power (in dBm) calculated by integrating the noise power over
the entire frequency sweep. The noise power at each frequency point is calculated by
multiplying the noise spectral density by a user-defined resolution bandwidth.
ns_pwr_ref_bw()
Returns noise power in a reference bandwidth
Syntax
y = ns_pwr_ref_bw(Sji, nf, resBW)
Arguments
284
Measurement Expressions
Name Description
Default Range Type
Required
Sji
complex transmission coefficient
None
(∞:∞)
Complex Yes
nf
noise figure at the output port (in
dB)
None
(∞:∞)
Complex Yes
resBW user-defined resolution bandwidth
None
(∞:∞)
Complex Yes
Examples
Y = ns_pwr_ref_bw(S21, nf2, 1MHz) returns the noise power with respect to the
reference bandwidth.
Defined in
$HPEESOF_DIR/expressions/ael/rf_system_fun.ael
See Also
ns_pwr_int() (expmeas), snr() (expmeas)
Notes/Equations
Used in Small-signal S-parameter simulation.
This is the noise power calculated by multiplying the noise spectral density at a frequency
point by a user-defined resolution bandwidth. Unlike NsPwrInt, this gives the noise power
(in dBm) at each frequency sweep.
The ns_pwr_ref_bw() function ignores noise from the load. It will always take into account
the noise from the source resistor to be fixed at 290K. You can raise the temperature of
the source resistor (Term), or set Noise to no in the source resistor (Term), or set Noise to
yes in the load resistor. These actions will not change the ns_pwr_ref_bw() results.
phase_comp()
Returns the phase compression (phase change)
Syntax
y = phase_comp(Sji)
Arguments
Name Description
Default Range Type
Required
Sji
None
Yes
power-dependent parameter obtained from large-signal
S-parameters simulation
Examples
a = phase_comp(S21[::, 0])
285
(∞:∞)
Integer, real,
complex
Measurement Expressions
Defined in
$HPEESOF_DIR/expressions/ael/rf_systems_fun.ael
See Also
gain_comp() (expmeas)
Notes/Equations
Used in Large-signal S-parameter simulations
This measurement calculates the small-signal minus the large-signal phase, in degrees.
The first power point (assumed to be small) is used to calculate the small-signal phase.
Phase compression (change) is only available for 1-D power sweep.
pwr_gain()
This measurement is used to determine the transducer power gain (in dB) and is defined
as the ratio of the power delivered to the load, to the power available from the source.
(where power is in dBm).
Syntax
y = pwr_gain(S, Zs, Zl, Zref)
Arguments
Name Description
Default Range Type
Required
S
2 X 2 scattering
matrix
None
(∞:∞)
Complex
Yes
Zs
input impedance
None
(∞:∞)
Real, Complex Yes
Zl
Output impedance
None
(∞:∞)
Real, Complex Yes
Zref
reference impedance
50.0
(∞:∞)
Real, Complex Yes
Examples
pGain = pwr_gain(S,50,75) - Zref defaults to 50 ohms
pGain1 = pwr_gain(S, 50, 75, 75) - Zref = 75 ohms
Defined in
$HPEESOF_DIR/expressions/ael/rf_system_fun.ael
See Also
286
Measurement Expressions
stos() (expmeas), volt_gain() (expmeas), volt_gain_max() (expmeas)
ripple()
This function measures the deviation of x from the average of x
Syntax
y = ripple(x, fstart, fstop)
Arguments
Name Description
Default Range Type Required
x
can be a gain or group delay data over a given frequency
range
None
(∞:∞)
Real Yes
fstart
start frequency
None
(0:∞)
Real No
fstop
stop frequency
None
(0:∞)
Real No
Examples
a = ripple(pwr_gain(S21))
a1 = ripple(pwr_gain(S21), 1GHz, 3GHz)
Defined in
$HPEESOF_DIR/expressions/ael/elementary_fun.ael
See Also
dev_lin_gain() (expmeas), dev_lin_phase() (expmeas), diff() (expmeas), mean()
(expmeas), phasedeg() (ael), phaserad() (ael), unwrap() (expmeas)
Notes/Equations
In order to use this function, the Group Delay option must be enabled in the S-parameter
analysis setup. For more information, refer to " Calculating Group Delay " in your " SParameter Simulation " documentation.
This function supports data up to four dimensions.
Note
The function name ripple() is used for more than one type of expression. For comparison, see the
Simulator Expression ripple() Expression (expsim). Also, for more information on the different expression
types and the contexts in which they are used, see Duplicated Expression Names (expmeas).
sm_gamma1()
Returns the simultaneous-match input-reflection coefficient.
Syntax
y = sm_gamma1(S)
287
Measurement Expressions
Arguments
Name Description
S
Default Range Type
scattering matrix of 2-port network None
(∞:∞)
Required
Complex Yes
Examples
a = sm_gamma1(S)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
max_gain() (expmeas), sm_gamma2() (expmeas), stab_fact() (expmeas), stab_meas()
(expmeas)
Notes/Equations
This complex measurement determines the reflection coefficient that must be presented to
the input (port 1) of the network to achieve simultaneous input and output reflections. If
the Rollett stability factor stab_fact(S) is less than unity for the analyzed circuit, then
sm_gamma1(S) returns 1+j*0.
sm_gamma2()
Returns the simultaneous-match output-reflection coefficient.
Syntax
y = sm_gamma2(S)
Arguments
Name Description
S
Default Range Type
scattering matrix of 2-port network None
(∞:∞)
Examples
a = sm_gamma2(S)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
288
Required
Complex Yes
Measurement Expressions
See Also
max_gain() (expmeas), sm_gamma1() (expmeas), stab_fact() (expmeas), stab_meas()
(expmeas)
Notes/Equations
This complex measurement determines the reflection coefficient that must be presented to
the output (port 2) of the network to achieve simultaneous input and output reflections. If
the Rollett stability factor stab_fact(S) is less than unity for the analyzed circuit, then
sm_gamma2(S) returns1+j*0.
sm_y1()
This complex measurement determines the admittance that must be presented to the
input (port 1) of the network to achieve simultaneous input and output reflections.
Syntax
y = sm_y1(S, Z)
Arguments
Name Description
Default Range Type
Required
S
scattering matrix of a 2-port
network
None
(∞:∞)
Complex
Yes
Z
port impedance
50.0
(∞:∞)
Integer, real or Complex Yes
Examples
a = sm_y1(S, 50)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
sm_y2() (expmeas)
sm_y2()
This complex measurement determines the admittance that must be presented to the
input (port 1) of the network to achieve simultaneous input and output reflections.
Syntax
y = sm_y2(S, Z)
Arguments
289
Measurement Expressions
Name Description
Default Range Type
Required
S
scattering matrix of a 2-port
network
None
(∞:∞)
Complex
Yes
Z
port impedance
50.0
(∞:∞)
Integer, real or Complex Yes
Examples
a = sm_y2(S, 50)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
sm_y1() (expmeas)
sm_z1()
This complex measurement determines the impedance that must be presented to the
input (port 1) of the network to achieve simultaneous input and output reflections.
Syntax
y = sm_z1(S, Z)
Arguments
Name Description
Default Range Type
Required
S
scattering matrix of a 2-port
network
None
(∞:∞)
Complex
Yes
Z
port impedance
50.0
(∞:∞)
Integer, real or Complex Yes
Examples
a = sm_z1(S, 50)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
sm_z2() (expmeas)
sm_z2()
This complex measurement determines the impedance that must be presented to the
output (port 2) of the network to achieve simultaneous input and output reflections.
290
Measurement Expressions
Syntax
y = sm_z2(S, Z)
Arguments
Name Description
Default Range Type
Required
S
scattering matrix of a 2-port
network
None
(∞:∞)
Complex
Yes
Z
port impedance
50.0
(∞:∞)
Integer, real or Complex Yes
Examples
a = sm_z2(S, 50)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
sm_z1() (expmeas)
s_stab_circle()
Returns source (input) stability circles.
Syntax
y = s_stab_circle(S, numOfPts)
Arguments
Name
Description
S
scattering matrix of a 2-port network. None
numOfPts desired number of points per circle
Default Range Type
51
Required
(∞:∞)
Complex Yes
[1:∞)
Integer
No
Examples
circleData = s_stab_circle(S, 51) returns the points on the circle(s).
Defined in
$HPEESOF_DIR/expressions/ael/circle_fun.ael
See Also
l_stab_circle() (expmeas), l_stab_region() (expmeas), s_stab_circle_center_radius()
291
Measurement Expressions
(expmeas), s_stab_region() (expmeas)
Notes/Equations
Used in Small-signal S-parameter simulations.
This expression generates source stability circles. The circles are defined by the loci of
source-reflection coefficients where the magnitude of the load-reflection coefficient is 1. A
circle is created for each value of the swept variable(s). This measurement is supported
for 2-port networks only.
To find the center and radius of the stability circle use the following expressions:
cir=s_stab_circle(S,2)
cir_center=sum((cir[0::1]) /2)
cir_radius=abs(cir[1]-cir[0]) /2
Alternately, the function s_stab_circle_center_radius() can be used. Use the function
s_stab_region(S) to determine the region of stability.
s_stab_circle_center_radius()
Returns the center and radius of the source stability circle
Syntax
s_cr = s_stab_circle_center_radius(S, Type)
Arguments
Name Description
Default Range
Type
Required
S
2-port S-Parameters
None
None
Complex Yes
Type
Type of parameter to
return
"both"
["both","center","radius"] String
No
Examples
1. s_cr=s_stab_circle_center_radius(S) returns a 1X2 matrix containing center
and radius
sCirc=expand(circle(s_cr(1), real(s_cr(2)), 51)) returns data for the source
stability circle
2. s_radius=s_stab_circle_center_radius(S, "radius") returns the radius
Defined in
$HPEESOF_DIR/expressions/ael/circle_fun.ael
See Also
l_stab_circle() (expmeas), s_stab_circle() (expmeas), l_stab_circle_center_radius()
(expmeas)
Notes/Equations
292
Measurement Expressions
Used in Small-signal S-parameter simulations
If the argument Type is not specified, the function returns complex data. Although radius
is of type real, the values are returned as complex. Therefore, when using the returned
radius, use the real part. To obtain the radius as a real number, set Type to radius .
s_stab_region()
This expression returns a string identifying the region of stability of the corresponding
source stability circle.
Syntax
y = s_stab_region(S)
Arguments
Name Description
S
Default Range Type
scattering matrix of a 2-port network. None
(∞:∞)
Required
Complex Yes
Examples
region = s_stab_region(S) returns "Outside" or "Inside".
Defined in
$HPEESOF_DIR/expressions/ael/circle_fun.ael
See Also
l_stab_circle() (expmeas), l_stab_region() (expmeas), s_stab_region() (expmeas)
Notes/Equations
Used in Small-signal S-parameter simulations
stab_fact()
Returns the Rollett stability factor.
Syntax
k = stab_fact(S)
Arguments
Name Description
S
Default Range Type
scattering matrix of 2-port network None
(∞:∞)
Examples
k = stab_fact(S)
293
Required
Complex Yes
Measurement Expressions
Defined in
$HPEESOF_DIR/expressions/ael/rf_system_fun.ael
See Also
max_gain() (expmeas), sm_gamma1() (expmeas), sm_gamma2() (expmeas),
stab_meas() (expmeas)
Notes/Equations
Given a 2 x 2 scattering matrix between the input and measurement ports, this function
calculates the stability factor. The Rollett stability factor is given by:
k = {1- |S11 |2- |S22 |2 + |S 11 *S22 - S12 *S21 |2} / {2*|S12 *S21 |}
The necessary and sufficient conditions for unconditional stability are that the stability
factor is greater than unity and the stability measure is positive.
Reference
1. Guillermo Gonzales, Microwave Transistor Amplifiers, second edition, Prentice-Hall,
1997.
stab_meas()
Returns the stability measure
Syntax
k = stab_meas(S)
Arguments
Name Description
S
Default Range Type
scattering matrix of 2-port network None
(∞:∞)
Complex Yes
Examples
k = stab_meas(S)
Defined in
$HPEESOF_DIR/expressions/ael/rf_system_fun.ael
294
Required
Measurement Expressions
See Also
max_gain() (expmeas), sm_gamma1() (expmeas), sm_gamma2() (expmeas), stab_fact()
(expmeas)
Notes/Equations
Given a 2 x 2 scattering matrix between the input and measurement ports, this function
calculates the stability measure. The stability measure is given by:
b = 1+ |S11 |2 - |S22 |2 - |S11 *S22 - S12 *S21 |2
The necessary and sufficient conditions for unconditional stability are that the stability
factor is greater than unity and the stability measure is positive.
Reference
1. Guillermo Gonzales, Microwave Transistor Amplifiers, second edition, Prentice-Hall,
1997.
stoabcd()
This measurement transforms the scattering matrix of a 2-port network to a chain (ABCD)
matrix
Syntax
y = stoabcd(S, zRef)
Arguments
Name Description
Default Range Type
Required
S
scattering matrix of a 2-port
network
None
(∞:∞)
Complex
Yes
zRef
reference impedance
50.0
(∞:∞)
Integer, real or
complex
No
Examples
a = stoabcd(S, 50)
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
See Also
abcdtoh() (expmeas), stoh() (expmeas), stoy() (expmeas)
stoh()
This measurement transforms the scattering matrix of a 2-port network to a hybrid matrix
295
Measurement Expressions
Syntax
y = stoh(S, zRef)
Arguments
Name Description
Default Range Type
Required
S
scattering matrix of a 2-port
network
None
(∞:∞)
Complex
Yes
zRef
reference impedance
50.0
(∞:∞)
Integer, real or
complex
No
Examples
h = stoh(S, 50)
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
See Also
htos() (expmeas), stoabcd() (expmeas), stoy() (expmeas)
stos()
Changes the normalizing impedance of a scattering matrix.
Syntax
y = stos(S, zRef, zNew, zy)
Arguments
Name Description
Default
Range Type
Required
S
scattering matrix
None
(∞:∞)
Complex
Yes
zRef
normalizing impedance
50.0
(∞:∞)
Integer, real or
complex
No
zNew
new normalizing impedance
50.0
(∞:∞)
Integer, real or
complex
No
zy
directs the conversion through the Z- or Ymatrix. †
1 (Ymatrix)
[0:1]
Integer
No
† f zy=0, the S-to-S conversion is performed through the Z-matrix. If zy=1, the S-to-S
conversion is performed through the Y-matrix
Examples
Converts the 50 ohm terminated S-parameters to 75 ohm terminated S-parameters
through the Y-matrix:
a = stos(S, 50, 75, 1)
Converts the 75 ohm terminated S-parameters to 50 ohm terminated S-parameters
296
Measurement Expressions
through the Y-matrix:
a = stos(S, 75)
Assume that a two-port S-parameter analysis has been done with port 1
terminated in50 ohms, and port 2 in 75 ohms. The expression below converts the
S-parameters at a 50 ohm impedance termination at both ports:
S50 = stos(S, PortZ, 50, 1)
The above converted S-parameters can than be written to a S2P file using the
function write_snp().
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
See Also
stoy() (expmeas), stoz() (expmeas)
stot()
This function transforms the scattering matrix of a 2-port network to a chain scattering
matrix.
Syntax
t = stot(S)
Arguments
Name Description
Default Range Type
S
None
scattering matrix of a 2-port
network
(∞:∞)
Required
Complex Yes
Examples
Tparams = stot(S)
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
See Also
ttos() (expmeas)
stoy()
This measurement transforms a scattering matrix to an admittance matrix.
Syntax
297
y = stoy(S, zRef)
Measurement Expressions
Arguments
Name Description
Default Range Type
Required
S
scattering matrix of a 2-port
network
None
(∞:∞)
Complex
Yes
zRef
reference impedance
50.0
(∞:∞)
Integer, real or
complex
No
Examples
y = stoy (S, 50.0)
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
See Also
stoh() (expmeas), stoz() (expmeas), ytos() (expmeas)
stoz()
This measurement transforms a scattering matrix to an impedance matrix.
Syntax
z = stoz(S, zRef)
Arguments
Name Description
Default Range Type
Required
S
scattering matrix of a 2-port
network
None
(∞:∞)
Complex
Yes
zRef
reference impedance
50.0
(∞:∞)
Integer, real or
complex
No
Examples
z = stoz(S, 50)
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
See Also
stoh() (expmeas), stoy() (expmeas), ztos() (expmeas)
tdr_step_impedance()
298
Measurement Expressions
Returns time domain Impedance. This function essentially takes
voltage reflection coefficient and calculates impedance versus time.
Syntax
y = tdr_step_impedance(VSource, Zref, Vincident)
Arguments
Name
Description
Default Range Type
Required
VSource Step voltage source
None
(∞:∞)
Complex Yes
zRef
None
[0:∞)
real
Vincident time domain pulse TDR waveform None
(∞:∞)
Complex Yes
Reference impedance
Yes
Examples
x = tdr_step_impedance(VSrc, 50, Vin)
Defined in
$HPEESOF_DIR/expressions/ael/DesignGuide_fun.ael
See Also
tdr_sp_gamma() (expmeas), tdr_sp_imped() (expmeas)
Notes/Equations
This function takes a time domain pulse TDR waveform, and computes the impedance
versus time. The function requires that a step impulse was applied to the DUT.
Use this function instead of tdr_step_imped() (expmeas).
tdr_sp_gamma()
Returns step response. This function calculates time domain response from the Sparameter measurement directly. Normalization is taken into account.
Syntax
y = tdr_sp_gamma(Sii, delay, Tstart, Tstop, NumPts, window)
Arguments
Name
Description
Default Range Type
Required
Sii
Complex reflection
coefficient
None
(∞:∞)
Complex
Yes
delay
delay value
None
[0:∞)
real
Yes
Tstart
Start Time
0
[0:∞)
real
No
Tstop
Stop Time
2 cycles [0:∞)
real
No
NumPts Number of points
101
[0:∞)
real ot string No
Window Windowing to be applied
0
[0:9] † real
No
† The window types allowed and their default constants are:
0 = None
299
Measurement Expressions
1 = Hamming 0.54
2 = Hanning 0.50
3 = Gaussian 0.75
4 = Kaiser 7.865
5 = 8510 6.0 (This is equivalent to the frequency-to-time transformation with
normal gate window setting in the 8510 series network analyzer.)
6 = Blackman
7 = Blackman-Harris
8 = 8510-Minimum 0
9 = 8510-Maximum 13
Examples
x = tdr_sp_gamma(S(1,1), 0.05ns, -0.2 ns, 3.8 ns, 401, "Hamming")
Defined in
$HPEESOF_DIR/expressions/ael/DesignGuide_fun.ael
See Also
tdr_sp_imped() (expmeas), tdr_step_imped() (expmeas)
Notes/Equations
This function takes an S-parameter dataset and changes it to a step response. The step
response is normalized and used to calculate reflection coefficient vs. time.
tdr_sp_imped()
Returns step response. This function calculates time domain response from the Sparameter measurement directly. Normalization is taken into account.
Syntax
y = tdr_sp_imped(Sii, delay, zRef, Tstart, Tstop, NumPts, window)
Arguments
Name
Description
Default Range Type
Required
Sii
Complex reflection
coefficient
None
(∞:∞)
Complex
Yes
delay
delay value
None
[0:∞)
real
Yes
zRef
Reference impedance
None
[0:∞)
real
Yes
Tstart
Start Time
0
[0:∞)
real
No
Tstop
Stop Time
2 cycles [0:∞)
real
No
NumPts Number of points
101
[0:∞)
real ot string No
Window Windowing to be applied
0
[0:7] † real
No
† The window types allowed and their default constants are:
300
Measurement Expressions
0 = None
1 = Hamming 0.54
2 = Hanning 0.50
3 = Gaussian 0.75
4 = Kaiser 7.865
5 = 8510 6.0 (This is equivalent to the frequency-to-time transformation with
normal gate window setting in the 8510 series network analyzer.)
6 = Blackman
7 = Blackman-Harris
8 = 8510-Minimum 0
9 = 8510-Maximum 13
Examples
x = tdr_sp_imped(S(1,1), 0.05ns, 50, -0.2 ns, 3.8 ns, 401, "Hamming")
Defined in
$HPEESOF_DIR/expressions/ael/DesignGuide_fun.ael
See Also
tdr_sp_gamma() (expmeas), tdr_step_imped() (expmeas)
Notes/Equations
This function takes an S-parameter dataset and changes it to a step response. The step
response is normalized and used to calculate reflection coefficient vs. time. This gamma is
then used to calculate impedance versus time.
tdr_step_imped()
Returns time domain Impedance. This function essentially takes
voltage reflection coefficient and calculates impedance versus time.
Syntax
y = tdr_step_imped(time_waveform, zRef)
Arguments
Name
Description
Default Range Type
Required
time_waveform time domain pulse TDR waveform None
(∞:∞)
Complex Yes
zRef
[0:∞)
real
Reference impedance
None
Examples
x = tdr_step_imped(vout, 50)
301
Yes
Measurement Expressions
Defined in
$HPEESOF_DIR/expressions/ael/DesignGuide_fun.ael
See Also
tdr_sp_gamma() (expmeas), tdr_sp_imped() (expmeas)
Notes/Equations
1. This function takes a time domain pulse TDR waveform, and computes the
impedance versus time. The function also assumes that a step impulse was applied to
the DUT, since it normalizes the impedance data to the last time point.
2. Please use tdr_step_impedance() (expmeas) function instead of this function.
ttos()
This function transforms the chain scattering matrix of a 2-port network to a scattering
matrix.
Syntax
sp = ttos(T)
Arguments
Name Description
Default Range Type
T
None
scattering matrix of a 2-port
network
(∞:∞)
Examples
sp = ttos(t)
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
See Also
stot() (expmeas)
unilateral_figure()
Returns the unilateral figure as a real number
Syntax
U = uniltaeral_figure(SParam)
302
Required
Complex Yes
Measurement Expressions
Arguments
Name
Description
Default Range Type
SParam 2-Port S-Parameters None
None
Required
Complex Yes
Examples
sMat={{polar(0.55,-50), polar(0.02,10)}, {polar(3.82,80),polar(0.15,-20)}}
U=uniltaeral_figure(sMat) returns 0.009
U_plus=10*log(1/(1-U)**2) returns 0.081
U_minus=10*log(1/(1+U)**2) returns -0.08
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
Notes/Equations
Used in Small-signal S-parameter simulations.
This function is used to calculate the Unilateral Figure of Merit, which determines whether
the simplification can be made in neglecting the effect of S12 (unilateral behavior of
device). It is calculated as:
The error limit on unilateral figure or merit, U is:
where:
GT is Transducer Gain
GTU is Unilateral Transducer Gain
This function can be used only with 2-Port S-parameters and works only on 1-dimensional
or single swept parameter data.
unwrap()
This measurement unwraps a phase by changing an absolute jump greater than jump to
its 2*jump complement
Syntax
y = unwrap(phase, jump)
Arguments
303
Measurement Expressions
Name Description
Default Range Type
Required
phase swept real
variable
None
(∞:∞)
Real
Yes
jump
180.0
(∞:∞)
Integer, Real No
absolute jump
Examples
a = unwrap(phase(S21))
a = unwrap(phaserad(S21), pi)
Defined in
Built-in
See Also
dev_lin_phase() (expmeas), diff() (expmeas), phase() (ael), phasedeg() (ael), phaserad()
(ael), ripple() (expmeas)
Notes/Equations
The unwrap function requires that the difference between two succesive data should be
less than or greater than 2*jump. Otherwise no jump is made for that phase and the
original data is maintained. And, if the number of phase data points is one, no phase is
unwrapped and the original data is maintained.
v_dc()
Returns the voltage difference.
Syntax
y = v_dc(vPlus, vMinus)
Arguments
Name Description
vPlus
Default Range Type
Required
voltage at the positive output terminal None
(∞:∞)
Real, Complex Yes
vMinus voltage at the negative output terminal None
(∞:∞)
Real, Complex Yes
Examples
y = v_dc(vp, vm)
Defined In
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
304
Measurement Expressions
volt_gain()
Returns the voltage gain
Syntax
y= volt_gain(S, Zs, Zl, Zref)
Arguments
Name Description
Default Range Type
Required
S
2 2 scattering matrix measured with equal terminations of
Zref
None
None
Complex
Yes
Zs
input impedance
None
(∞:∞)
Real,
Complex
Yes
Zl
Output impedance
None
(∞:∞)
Real,
Complex
Yes
Zref
reference impedance
50.0
(∞:∞)
Real,
Complex
Yes
Examples
a = volt_gain(S, 50, 75)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
pwr_gain() (expmeas), volt_gain_max() (expmeas)
Notes/Equations
This function calculates the ratio of the voltage across the load impedance to the voltage
applied at the input port of the network. The network-parameter transformation function
stos() can be used to change the normalizing impedance of the scattering matrix.
Signal Flow Diagram used for volt_gain Calculation illustrates the volt_gain measurement.
305
Measurement Expressions
Signal Flow Diagram used for volt_gain Calculation
1. In the S-parameter simulation setup, the source and load impedances must be
identical.
2. For a case of unequal source and load impedances, S-parameter analysis should be
performed with identical source and load impedances. Voltage gain can then be
computed with the actual source and load impedances as the second and third
arguments.
For example, compute voltage gain with Zs=100 and Zl=50. Perform an S-parameter
analysis with both the Zs=Zl=50 ohms. The voltage gain is computed as follows:
volt_gain(S, 100, 50, 50)
This expression gives the voltage gain when the source impedance is 100 ohms and
the load impedance is 50 ohms. The fourth argument in volt_gain is the reference
impedance, which is the value of the Z parameter of the Term components used in
the S-parameter analysis.
volt_gain_max()
This measurement determines the ratio of the voltage across the load to the voltage
available from the source at maximum power transfer.
Syntax
y = volt_gain_max(S, Zs, Zl, Zref)
Arguments
Name Description
Default Range Type
Required
S
2 X 2 scattering
matrix
None
(∞:∞)
Complex
Yes
Zs
input impedance
None
(∞:∞)
Real, Complex Yes
Zl
Output impedance
None
(∞:∞)
Real, Complex Yes
Zref
reference impedance
50.0
(∞:∞)
Real, Complex Yes
Examples
vGain = volt_gain_max(S,50,75) - Zref defaults to 50 ohms
vGain1 = volt_gain(S, 50, 75, 75) - Zref = 75 ohms
306
Measurement Expressions
Defined in
$HPEESOF_DIR/expressions/ael/rf_system_fun.ael
See Also
pwr_gain() (expmeas), volt_gain() (expmeas)
Note/Equations
The network-parameter transformation function stos() can be used to change the
normalizing impedance of the scattering matrix.
vswr()
Given a complex reflection coefficient, this measurement returns the voltage standing
wave ratio.
Syntax
y = vswr(Sii)
Arguments
Name Description
Default Range Type
Sii
None
complex reflection
coefficient
(∞:∞)
Required
Complex Yes
Examples
y = vswr(S11)
Defined in
$HPEESOF_DIR/expressions/ael/rf_system_fun.ael
See Also
yin() (expmeas), zin() (expmeas)
write_snp()
Write S-Parameters in Touchstone SnP file format. Returns True or False.
Syntax
y = write_snp(FileName, S, Comment, FreqUnit, DataFormat, Zref, Znorm, ZorY,
Precision, Delimiter)
307
Measurement Expressions
Arguments
Name
Description
Default
Range
Type
Required
FileName
Name or full-path of the SParameter file.
None
None
String
Yes
S
S-parameter matrix variable
None
None
Real,
Complex
Yes
Comment
Text that is to be written at the top
of file.
""
None
String
No
FreqUnit
Frequency Unit
GHz
"Hz", "KHz", "MHz",
"GHz", "THz"
String
No
DataFormat Format of S-Parameter that is to be
output
"MA"
"MA", "DB", "RI" †
String
No
Zref
Reference impedance (scalar or
vector)
50
(0:∞)
Real
No
Znorm
Normalizing impedance (a scalar
value)
50
(0:∞)
Real
No
ZorY
Directs the conversion through Z or
Y transform ††
1 (Ymatrix)
[0:1]
Integer
No
Precision
precision of the data
6
[1:64]
Integer
No
Delimiter
Delimiter that separates the data
"\t"
None
String
No
† "MA" = magnitude-phase, "DB" = dB-phase, "RI" = real-imaginary
†† If ZorY=0, the S-to-S conversion is performed through the Z-matrix. If ZorY=1, the Sto-S conversion is performed through the Y-matrix
Examples
We assume that a S-Parameter Analysis has been performed.
write_snp("spar_ts.s2p", S, "S-par simulation data", "GHz", "MA", 50)
writes the S-Parameters to the file spar_ts.s2p in mag-phase format
write_snp("spar_ts_1.s2p", S, "S-par simulation data")
writes the S-Parameters to the file spar_ts_1.s2p in default "GHz", mag-phase
format and referenece impedance of 50.0.
We assume that a 2-port S-Parameter Analysis has been performed with source
terminated in 60 ohms and load terminated in 70 ohms:
write_snp("spar_norm_ts.s2p", S, "S-par simulation data", "GHz", "MA", PortZ,
50, 1,9," ")
writes the S-Parameters to the file spar_norm_ts.s2p in "GHz", mag-phase
format, with 9 digit precision and delimited by " " and normalized impedance of
50.0.
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
See Also
stos() (expmeas)
308
Measurement Expressions
Notes/Equations
The function supports only 1-dimensional S-parameter data. S-parameters can be from 1
to 99 ports. The S-parameters to be written can be normalized by a different impedance
through the arguments Znorm and ZorY . If the argument Znorm is not specified, then the
S-parameters are normalized to 50 ohms.
When using this function from the schematic page, the output file will be written in the
workspace data directory. When used from the Data Display, the file will be written to the
workspace directory.
yin()
Given a reflection coefficient and the reference impedance, this measurement returns the
input admittance looking into the measurement ports.
Syntax
y = yin(Sii, Z)
Arguments
Name Description
Default Range Type
Required
Sii
complex reflection
coefficient
None
(∞:∞)
Complex
Yes
zRef
reference impedance
50.0
(∞:∞)
Integer, real or
complex
No
Examples
yIN = yin(S11, 50)
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
See Also
vswr() (expmeas), zin() (expmeas)
yopt()
Returns optimum admittance for noise match
Syntax
y = yopt(gammaOpt, zRef)
Arguments
309
Measurement Expressions
Name
Description
Default Range Type
Required
gammaOpt optimum reflection coefficient None
(∞:∞)
Complex
zRef
(∞:∞)
Real, Complex No
reference impedance
50.0
Yes
Examples
a = yopt(Sopt, 50)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
zopt() (expmeas)
Notes/Equations
Used in Small-signal S-parameter simulations
This complex measurement produces the optimum source admittance for noise matching.
gammaOpt is the optimum reflection coefficient that must be presented at the input of the
network to realize the minimum noise figure (NFmin).
ytoabcd()
This measurement transforms an admittance matrix of a 2-port network into a hybrid
matrix.
Syntax
a = ytoabcd(Y)
Arguments
Name Description
Y
Default Range Type
2-port admittance matrix None
(∞:∞)
Required
Complex Yes
Examples
a = ytoabcd(Y)
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
310
Measurement Expressions
See Also
abcdtoh() (expmeas), htoabcd() (expmeas)
ytoh()
This measurement transforms an admittance matrix of a 2-port network into a hybrid
matrix.
Syntax
h = ytoh(Y)
Arguments
Name Description
Y
Default Range Type
2-port admittance matrix None
(∞:∞)
Required
Complex Yes
Examples
h = ytoh(Y)
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
See Also
htoy() (expmeas), ytoabcd() (expmeas)
ytos()
This measurement transforms an admittance matrix into a scattering matrix.
Syntax
z = ytos(Y, zRef)
Arguments
Name Description
Default Range Type
Required
Y
admittance matrix
None
(∞:∞)
Complex
Yes
zRef
reference
impedance
50.0
(∞:∞)
Integer, real or
complex
No
Examples
s = ytos(Y, 50.0)
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
311
Measurement Expressions
See Also
stoy() (expmeas), ytoz() (expmeas)
ytoz()
This measurement transforms an admittance matrix to an impedance matrix.
Syntax
Z = ytoz(Y)
Arguments
Name Description
Default Range Type
Y
None
admittance
matrix
(∞:∞)
Required
Complex Yes
Examples
Z = ytoz(Y)
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
See Also
ytos() (expmeas), ztoy() (expmeas)
zin()
Given a reflection coefficient and the reference impedance, this measurement returns the
input impedance looking into the measurement ports.
Syntax
z = zin(Sii, Z)
Arguments
Name Description
Default Range Type
Required
Sii
complex reflection coefficient. None
(∞:∞)
Complex
Yes
zRef
reference impedance
(∞:∞)
Integer, real or
complex
No
50.0
Examples
zIN = zin(S11, 50.0)
312
Measurement Expressions
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
See Also
vswr() (expmeas), yin() (expmeas)
zopt()
Returns optimum impedance for noise match
Syntax
y = zopt(gammaOpt, zRef)
Arguments
Name
Description
Default Range Type
Required
gammaOpt optimum reflection coefficient None
(∞:∞)
Complex
zRef
(∞:∞)
Real, Complex No
reference impedance
50.0
Yes
Examples
a = zopt(Sopt, 50)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
yopt() (expmeas)
Notes/Equations
Used in Small-signal S-parameter simulations.
This complex measurement produces the optimum source impedance for noise matching.
gammaOpt is the optimum reflection coefficient that must be presented at the input of the
network to realize the minimum noise figure (NFmin).
ztoabcd()
This measurement transforms an impedance matrix of a 2-port network into a chain
(ABCD) matrix.
Syntax
313
Measurement Expressions
a = ztoabcd(Z)
Arguments
Name Description
Default Range Type
Z
None
2-port impedance
matrix
(∞:∞)
Required
Complex Yes
Examples
a = ztoabcd(Z)
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
See Also
abcdtoz() (expmeas), ytoabcd() (expmeas), ztoh() (expmeas)
ztoh()
This measurement transforms an impedance matrix of a 2-port network into a hybrid
matrix.
Syntax
h = ztoh(Z)
Arguments
Name Description
Default Range Type
Z
None
2-port impedance
matrix
(∞:∞)
Required
Complex Yes
Examples
h = ztoh(Z)
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
See Also
htoz() (expmeas), ytoh() (expmeas), ztoabcd() (expmeas)
ztos()
This measurement transforms an impedance matrix to a scattering matrix.
314
Measurement Expressions
Syntax
sp = ztos(Z, zRef)
Arguments
Name Description
Default Range Type
Required
Z
impedance matrix
None
(∞:∞)
Complex
Yes
zRef
reference
impedance
50.0
(∞:∞)
Integer, real or
complex
No
Examples
s = ztos(Z, 50.0)
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
See Also
stoz() (expmeas), ytoz() (expmeas), ztoy() (expmeas)
ztoy()
This measurement transforms an impedance matrix to an admittance matrix.
Syntax
y = ztoy(Z)
Arguments
Name Description
Default Range Type
Z
None
impedance
matrix
(∞:∞)
Required
Complex Yes
Examples
y = ztoy(Z)
Defined in
$HPEESOF_DIR/expressions/ael/network_fun.ael
See Also
stoz() (expmeas), ytos() (expmeas), ztoy() (expmeas)
315
Measurement Expressions
Statistical Analysis Functions
This section describes the statistical analysis functions in detail. The functions are listed in
alphabetical order.
cdf() (expmeas)
cross corr() (expmeas)
fun 2d outer() (expmeas)
histogram() (expmeas)
histogram multiDim() (expmeas)
histogram sens() (expmeas)
histogram stat() (expmeas)
interpolate swept data() (expmeas)
interpolate_swept_data_Xdb()
lognorm dist1D() (expmeas)
lognorm dist inv1D() (expmeas)
mean() (expmeas)
mean outer() (expmeas)
median() (expmeas)
moving average() (expmeas)
norm dist1D() (expmeas)
norm dist inv1D() (expmeas)
norms dist1D() (expmeas)
norms dist inv1D() (expmeas)
pdf() (expmeas)
stddev() (expmeas)
stddev outer() (expmeas)
uniform dist1D() (expmeas)
uniform dist inv1D() (expmeas)
yield sens() (expmeas)
cdf()
Returns the cumulative distribution function (CDF)
Syntax
y = cdf(data, numBins, minBin, maxBin)
Arguments
Name
Description
Default
Range Type Required
data
the signal
None
(∞:∞)
Real Yes
numBins number of subintervals or bins used to
measure CDF
log(numOfPts)/log(2.0)
[1:∞)
Real No
minBin
beginning of the evaluation of the CDF
minimum value of the
data
(∞:∞)
Real No
maxBin
end of the evaluation of the CDF
maximum value of the
data
(∞:∞)
Real No
Examples
y = cdf(data)
y = cdf(data, 20)
316
Measurement Expressions
Defined in
$HPEESOF_DIR/expressions/ael/statistical_fun.ael
See Also
histogram() (expmeas), pdf() (expmeas), yield_sens() (expmeas)
Notes/Equations
This function measures the cumulative distribution function of a signal. This function can
only be used by entering an equation (Eqn) in the Data Display window.
cross_corr()
Returns the cross-correlation
Syntax
y = cross_corr(v1, v2)
Arguments
Name Description
Default Range Type Required
v1
one-dimensional data None
(∞:∞)
Real Yes
v2
one-dimensional data None
(∞:∞)
Real Yes
Examples
v1 = qpsk..videal[1]
v2 = qpsk..vout[1]
x_corr_v1v2 = cross_corr(v1, v2)
auto_corr_v1 = cross_corr(v1, v1)
Defined in
$HPEESOF_DIR/expressions/ael/digital_wireless_fun.ael
fun_2d_outer()
Applies a function to the outer dimension of two-dimensional data
Syntax
y = fun_2d_outer(data, fun)
Arguments
317
Measurement Expressions
Name Description
Default Range Type
Required
data
two-dimensional data
None
fun
name of function (usually mean, max, or min) that will be None
applied to the outer dimension of the data
(∞:∞)
Integer, Real,
Complex
Yes
None
string
Yes
Examples
y = fun_2d_outer(data, min)
Defined in
$HPEESOF_DIR/expressions/ael/statistcal_fun.ael
See Also
max_outer() (expmeas), mean_outer() (expmeas), min_outer() (expmeas)
Notes/Equations
Used in max_outer(), mean_outer(), min_outer() functions.
Functions such as mean, max, and min operate on the inner dimension of two-dimensional
data. The function fun_2d_outer enables these functions to be applied to the outer
dimension. As an example, assume that a Monte Carlo simulation of an amplifier was run,
with 151 random sets of parameter values, and that for each set the S-parameters were
simulated over 26 different frequency points. S21 becomes a [151 Monte Carlo iteration X
26 frequency] matrix, with the inner dimension being frequency, and the outer dimension
being Monte Carlo index. Now, assume that it is desired to know the mean value of the Sparameters at each frequency. Inserting an equation mean(S21) computes the mean
value of S21 at each Monte Carlo iteration. If S21 is simulated from 1 to 26 GHz, it
computes the mean value over this frequency range, which usually is not very useful. The
function fun_2d_outer allows the mean to be computed over each element in the outer
dimension.
histogram()
Generates a histogram representation. This function creates a histogram that represents
data
Syntax
y = histogram(data, numBins, minBin, maxBin)
Arguments
318
Measurement Expressions
Name
Description
Default
Range Type
Required
data
signal(must be one-dimensional)
None
(∞:∞)
Integer,
Real
Yes
numBins number of subintervals or bins used to
measure the histogram.
log(numOfPts)/log(2.0)
[1:∞)
Integer
No
minBin
beginning of the evaluation of the
histogram
minimum value of the
data
(∞:∞)
Real
No
maxBin
end of the evaluation of the histogram
maximum value of the
data
(∞:∞)
Real
No
Examples
y = histogram(data)
y = histogram(data, 20)
If you have performed a parameter sweep such that the first argument (data) in
the histogram function is a function of two independent variables, then you
must reduce the dimensionality of data before using it in the histogram
function. For example, if you run a Monte Carlo simulation on the S-parameters
of a circuit, S21 would be a function of both the Monte Carlo index and the
frequency (assuming you have swept frequency).
So, you could plot the histogram of S21 at the 100th frequency in the sweep by
using:
y = histogram(dB(S21[::,99]))
See also $HPEESOF_DIR/examples/Tutorial/yldex1_wrk
(see measurement_hist.dds and worstcase_measurement_hist.dds)
Defined in
Built in
See Also
cdf() (expmeas), pdf() (expmeas), yield_sens() (expmeas), histogram_multiDim()
(expmeas), histogram_stat() (expmeas)
Notes/Equations
This function can only be used by entering an equation (Eqn) in the Data Display window.
Use the histogram_multiDim() function for multi-dimensional data.
histogram_multiDim()
Collapses the multi-dimensional data down to one-dimensional data and applies the
histogram to the one-dimensional data.
Syntax
y = histogram_multiDim(data, normalized, numBins, minBin, maxBin)
Arguments
319
Measurement Expressions
Name
Description
Default
Range
Type Required
data
the signal
None
(-∞:∞)
Real
normalized sets normalization of data †
no
"no",
"yes"
String No
numBins
number of subintervals or bins used to
measure CDF
log(numOfPts)/log(2.0)
[1:∞)
Real
No
minBin
beginning of the evaluation of the CDF
minimum value of the
data
(-∞:∞)
Real
No
maxBin
end of the evaluation of the CDF
maximum value of the
data
(-∞:∞)
Real
No
Yes
† When normalized is set to "yes", the histogram is generated with percent on the Y-axis
instead of the number of outcomes.
Examples
Given monte carlo analysis results for the S12. It is two-dimensional data: the
outer sweep is mcTrial; the inner sweep is the frequency from 100 MHz to 500
MHz.
Histogram_multiDim_S12 = histogram_multiDim(S12)
See also $HPEESOF_DIR/examples/Tutorial/yldex1_wrk
(see measurement_hist.dds and worstcase_measurement_hist.dds)
Defined in
$HPEESOF_DIR/expressions/ael/statistical_fun.ael
See Also
collapse() (expmeas), histogram() (expmeas)
histogram_sens()
Produces the yield sensitivity histogram displaying the sensitivity of a measurement
statistical response to a selected statistical variable. The function is mainly applied to the
statistical analysis (Monte Carlo/Yield/YieldOpt) results.
Syntax
y = histogram_sens(data, sensitivityVar, goalMin, goalMax, innermostIndepLow,
innermostIndepHigh, numBins)
Arguments
320
Measurement Expressions
Name
Description
Default
Range Type Required
data
statistical response
None
(∞:∞)
Real
sensitivityVar
selected statistical variable
None
None
String Yes
goalMin
specifies the performance range †
None
(∞:∞)
Real
No
goalMax
specifies the performance range †
None
(∞:∞)
Real
No
innermostIndepLow specifies the low value of the subrange None
of data with the inner most sweep
variable
(∞:∞)
Real
Yes
innermostIndepHigh specifies the high value of the
subrange of data with the inner most
sweep variable
None
(∞:∞)
Real
Yes
numBins
log(numOfPts)/log(2.0) (1:∞)
Real
No
number of sub-intervals or bins used
to measure the histogram.
Yes
† The yield is 1 inside the range, and the yield is zero outside the range. Note that while
goalMin and goalMax are optional arguments, at least one of them must be specified.
Examples
Given monte carlo analysis results for the S11. It is two-dimensional data: the
outer sweep is mcTrial; the inner sweep is the frequency from 100 MHz to 500
MHz.
The design wants the maximum of db(S11) is -18.0dB in the frequency range of
200 MHz to 400 MHz. The yield sensitivity of such performance to statistical
variable "C1v" can be calculated as:
Histogram_sens_S11 = histogram_sens(dB(S11),C1v,,-18.0,200MHz,400MHz)
Defined in
$HPEESOF_DIR/expressions/ael/statistical_fun.ael
See Also
histogram() (expmeas), histogram_multiDim() (expmeas), histogram_stat() (expmeas),
build_subrange() (expmeas), yield_sens() (expmeas)
histogram_stat()
Reduces the histogram of a subrange of the multi-dimension data. It first calls
build_subrange() to build the subrange of a mulit-dimension data, then calls
histogram_multiDim() to produce the histogram.
Syntax
y = histogram_stat(data, normalized, innermostIndepLow, innermostIndepHigh, numBins,
minBin, maxBin)
Arguments
321
Measurement Expressions
Name
Description
Default
Range
Type Required
data
statistical data to be analyzed
None
(-∞:∞) Real
normalized
sets normalization of data †
no
"no",
"yes"
innermostIndepLow specifies the low value of the
subrange of data with the inner
most sweep variable
None
(-∞:∞) Real
Yes
innermostIndepHigh specifies the high value of the
subrange of data with the inner
most sweep variable
None
(-∞:∞) Real
Yes
Yes
String No
numBins
number of subintervals or bins used log(numOfPts)/log(2.0)
to measure histogram
[1:∞)
Real
No
minBin
beginning of the evaluation of the
histogram
minimum value of the
data
(-∞:∞) Real
No
maxBin
end of the evaluation of the
histogram
maximum value of the
data
(-∞:∞) Real
No
† When normalized is set to "yes", the histogram is generated with percent on the Y-axis
instead of the number of outcomes.
Examples
Given monte carlo analysis results for the S12. It is two-dimensional data: the
outer sweep is mcTrial; the inner sweep is the frequency from 100 MHz to 500
MHz.
Histogram_stat_S12 = histogram_stat(S12,,200MHz,400MHz)
Defined in
$HPEESOF_DIR/expressions/ael/statistical_fun.ael
See Also
histogram() (expmeas), histogram_multiDim() (expmeas), build_subrange() (expmeas)
interpolate_swept_data()
Returns a function or trace's y-axis value or values corresponding to a specific x-axis
value
Syntax
Interpolated_Pout=interpolate_swept_data(original_data_Y_vs_X, desired_X,
interpStepSize, interpType)
Arguments
322
Measurement Expressions
Name
Description
Default Range
Type
Required
None
(-∞:∞)
Real
Yes
desired_X
X-axis search value, a single real or None
integer number
(-∞:∞)
Real or
Integer
Yes
interpStepSize
interpolation step size, a single real 0.05
or integer number
(-∞:∞)
Real or
Integer
No
interpType
type of interpolation
"linear", "spline",
or "cubic"
String
Yes
original_data_Y_vs_X one-, two-, or three-dimensional
data
None
Examples
Pout=dBm(Vload_fundHB)
Pin=indep(Vload_fundHB)
Gain_HB=Pout-Pin
Gain_vs_Pout=vs(Gain,Pout)
Search_Value=30
interpStepSize=0.05
interpType="spline"
Gain_at_Specified_Pout=interpolate_swept_data(Gain_vs_Pout, Search_Value,
interpStepSize, interpType)
Notes/Equations
This function would be useful for the following application. You have run a swept input
power simulation of an amplifier.
You plot a trace that is gain versus output power or gain compression versus output
power. Use this function to find the gain or gain compression at a particular output power.
This function is applicable even if you have run a Monte Carlo analysis or swept some
parameter. It enables you to see the distribution of the gain or gain compression when the
amplifier is delivering a
particular output power.
lognorm_dist_1D()
Returns a lognormal distribution: either its probability density function (pdf), or
cumulative distribution function (cdf).
Syntax
y = lognorm_dist1D(data, m, s, absS, is_cpf)
Arguments
Name Description
Default Range
Type
Required
data
number or a one-dimensional data
None
(-∞:∞)
Real
Yes
m
mean for the lognormal distribution
None
(-∞:∞)
Integer, Real Yes
s
standard deviation for the lognormal
distribution
None
(-∞:∞)
Integer, Real Yes
absS
specifies absolute or relative standard deviation 1
[0:∞) †
Integer
No
[0:∞) †
†
Integer
No
is_cpf specifies cdf or pdf og lognormal distribution
0
† When absS is not equal to "0", s is the absolute standard deviation; otherwise, s is the
relative standard deviation
† † When is_cdf is not equal to "0", the function returns the cdf of the lognormal
323
Measurement Expressions
distribution. Otherwise, it returns the pdf of the lognormal distribution.
Examples
X = 0.5
X_pdf= lognorm_dist1D(X, 2.0,0.2, 1, 0)
X_cdf = lognorm_dist1D(X,2.0,0.1, 0, 1)
XX=[-3.9::0.1::3.9]
XX_pdf = lognorm_dist1D(XX,2.0, 0.2,1,0)
XX_cdf = lognorm_dist1D(XX,2.0,0.2,0,1)
Defined in
$HPEESOF_DIR/expressions/ael/statistical_fun.ael
lognorm_dist_inv1D()
Returns the inverse of the cumulative distribution function (cdf) for a lognormal
distribution
Syntax
y = lognorm_dist_inv1D(data, m, s, absS)
Arguments
Name Description
Default Range Type
Required
data
real number representing the cumulative
probability
None
[0:1]
Yes
m
mean for the lognormal distribution
None
(-∞:∞) Integer, Real Yes
s
standard deviation for the lognormal distribution
None
(-∞:∞) Integer, Real Yes
absS
specifies absolute or relative standard deviation
1
[0:∞)
†
Real
Integer
No
† absS is not equal to "0", s is the absolute standard deviation; otherwise, s is the relative
standard deviation
Examples
X_cpf = 0.5
X= lognorm_dist_inv1D(X_cpf, 2.0, 0.2, 1)
XX_cpf=[0.0::0.01::1.0]
XX= lognorm_dist_inv1D(XX_cpf, 2.0, 0.2, 1)
Defined in
$HPEESOF_DIR/expressions/ael/statistical_fun.ael
mean()
Returns the mean
Syntax
324
Measurement Expressions
y = mean(x)
Arguments
Name Description
x
Default Range Type
data to find mean None
(∞:∞)
Required
Integer, Real, Complex Yes
Examples
a = mean([1, 2, 3]) returns 2
Defined in
Built in
See Also
cum_prod() (expmeas), cum_sum() (expmeas), max() (expmeas), min() (expmeas),
prod() (expmeas), sum() (expmeas)
mean_outer()
Computes the mean across the outer dimension of two-dimensional data
Syntax
y = mean_outer(data)
Arguments
Name Description
data
Default Range Type
2-dimensional data to find mean None
(∞:∞)
Required
Integer, Real, Complex Yes
Examples
a = mean_outer(data)
Defined in
$HPEESOF_DIR/expressions/ael/statistcal_fun.ael
See Also
fun_2d_outer() (expmeas), max_outer() (expmeas), min_outer() (expmeas)
Notes/Equations
325
Measurement Expressions
The mean function operates on the inner dimension of two-dimensional data. The
mean_outer function just calls the fun_2d_outer function, with mean being the applied
operation. As an example, assume that a Monte Carlo simulation of an amplifier was run,
with 151 random sets of parameter values, and that for each set the S-parameters were
simulated over 26 different frequency points. S21 becomes a [151 Monte Carlo iteration X
26 frequency] matrix, with the inner dimension being frequency, and the outer dimension
being Monte Carlo index. Now, assume that it is desired to know the mean value of the Sparameters at each frequency. Inserting an equation mean(S21) computes the mean
value of S21 at each Monte Carlo iteration. If S21 is simulated from 1 to 26 GHz, it
computes the mean value over this frequency range, which usually is not very useful.
Inserting an equation mean_outer(S21) computes the mean value of S21 at each Monte
Carlo frequency.
median()
Returns the median
Syntax
y = median(x)
Arguments
Name Description
Default Range Type Required
data
None
data to find the
median
(∞:∞)
Real Yes
Examples
a = median([1, 2, 3, 4]) returns 2.5
Defined in
$HPEESOF_DIR/expressions/ael/statistcal_fun.ael
See Also
mean() (expmeas), sort() (expmeas)
Notes/Equations
This function can only be used by entering an equation (Eqn) in the Data Display window.
moving_average()
Returns the moving_average of a sequence of data
Syntax
y = moving_average(Data, NumPoints)
Arguments
326
Measurement Expressions
Name
Description
Default Range Type
Required
Data
one or multi-dimensional sequence of
numbers
None
(-∞:∞) Integer, real or
complex
Yes
None
[1:∞)
†
Yes
NumPoints Number of points to be averaged together
Integer
† NumPoints must be an odd number. If even, the value is
increased to the next odd number. If greater or equal to the number of data
points, the value is set to number of data points - 1 for even number of data
points. For odd number of data points, NumPoints is set to number of data points.
Examples
a = moving_average([1, 2, 3, 7, 5, 6, 10], 3) returns [1, 2, 4, 5, 6, 7, 10]
Defined in
Built in
Notes/Equations
The first value of the smoothed sequence is the same as the original data. The second
value is the average of the first three. The third value is the average of data elements 2,
3, and 4, etc. If NumPoints were set to 7, for example, then the first value of the
smoothed sequence would be the same as the original data. The second value would be
the average of the first three original data points. The third value would be the average of
the first five data points, and the fourth value would be the average of the first seven data
points. Subsequent values in the smoothed array would be the average of the seven
closest neighbors. The last points in the smoothed sequence are computed in a way
similar to the first few points. The last point is just the last point in the original sequence.
The second from last point is the average of the last three points in the original sequence.
The third from the last point is the average of the last five points in the original sequence,
etc.
norm_dist_1D()
Returns a normal distribution: either its probability density function (pdf), or cumulative
distribution function (cdf)
Syntax
y = norm_dist1D(data, m, s, absS, is_cdf)
Arguments
327
Measurement Expressions
Name Description
Default Range
Type
Required
data
number or a one-dimensional data
None
(-∞:∞)
Real
Yes
m
mean for the normal distribution
None
(-∞:∞)
Integer, Real Yes
s
standard deviation for the normal distribution
None
(-∞:∞)
Integer, Real Yes
absS
specifies absolute or relative standard
deviation
1
[0:∞) †
Integer
No
0
[0:∞) †
†
Integer
No
is_cdf specifies cdf or pdf of normal distribution
† When absS is not equal to "0", s is the absolute standard deviation; otherwise, s is the
relative standard deviation
† † When is_cdf is not equal to "0", the function returns the cdf of the normal distribution.
Otherwise, it returns the pdf of the normal distribution.
Examples
X = 0.5
X_pdf= norm_dist1D(X, 0, 1, 1, 0)
X_cdf = norm_dist1D(X,0, 1, 1, 1)
XX=[-3.9::0.1::3.9]
XX_pdf = norm_dist1D(XX,5.0, 0.5,1,0)
XX_cdf = norm_dist1D(XX,5.0,0.1,0,1)
Defined in
$HPEESOF_DIR/expressions/ael/statistical_fun.ael
See Also
norm_dist_inv1D() (expmeas), norms_dist_inv1D() (expmeas), norms_dist1D()
(expmeas), lognorm_dist_inv1D() (expmeas), lognorm_dist1D() (expmeas),
uniform_dist_inv1D() (expmeas), uniform_dist1D() (expmeas)
norm_dist_inv1D()
Returns the inverse of the cumulative distribution function (cdf) for a normal distribution
Syntax
y = norm_dist_inv1D(data, m, s, absS)
Arguments
Name Description
Default Range Type
Required
data
represents the cumulative probability
None
[0:1]
Yes
m
mean for the normal distribution
None
(-∞:∞) Integer, Real Yes
s
standard deviation for the normal distribution
None
(-∞:∞) Integer, Real Yes
absS
specifies absolute or relative standard
deviation
1
[0:∞)
†
Real
Integer
No
† When absS is not equal to "0", s is the absolute standard deviation; otherwise, s is the
328
relative standard deviation
Measurement Expressions
Examples
X_cpf = 0.5
X= norm_dist_inv1D(X_cpf, 0, 1, 1) will be equal to 0.0
XX_cpf=[0.0::0.01::1.0]
XX= norm_dist_inv1D(XX_cpf, 5.0, 0.5, 1)
Defined in
$HPEESOF_DIR/expressions/ael/statistical_fun.ael
See Also
norm_dist1D() (expmeas), norms_dist_inv1D() (expmeas), norms_dist1D() (expmeas),
lognorm_dist_inv1D() (expmeas), lognorm_dist1D() (expmeas), uniform_dist_inv1D()
(expmeas), uniform_dist1D() (expmeas)
norms_dist1D()
Returns the standard normal distribution: either its probability density function (pdf), or
cumulative distribution function (cdf).
Syntax
y = norms_dist1D(data, is_cdf)
Arguments
Name Description
Default Range Type
Required
data
None
Yes
number or a one-dimensional data
is_cdf specifies cdf or pdf of standard normal distribution 0
(-∞:∞) Real
[0:∞)
†
Integer No
† When is_cdf is not equal to "0", the function returns the cdf of the standard normal
distribution. Otherwise, it returns the pdf of the standard normal distribution.
Examples
X = 0.5
X_pdf= norms_dist1D(X, 0)
X_cdf = norms_dist1D(X,1)
XX=[-3.9::0.1::3.9]
XX_pdf = norms_dist1D(XX,0)
XX_cdf = norms_dist1D(XX,1)
Defined in
$HPEESOF_DIR/expressions/ael/statistical_fun.ael
329
Measurement Expressions
See Also
norm_dist1D() (expmeas), norm_dist_inv1D() (expmeas), norms_dist_inv1D()
(expmeas), lognorm_dist_inv1D() (expmeas), lognorm_dist1D() (expmeas),
uniform_dist_inv1D() (expmeas), uniform_dist1D() (expmeas)
norms_dist_inv1D()
Returns the inverse of the cumulative distribution function (cdf) for a standard normal
distribution
Syntax
y = norms_dist_inv1D(data)
Arguments
Name Description
data
Default Range Type
number represents the cumulative probability None
[0:1]
Required
Integer, Real Yes
Examples
X_cpf = 0.5
X= norms_dist_inv1D(X_cpf) will be equal to 0.0
XX_cpf=[0.0::0.01::1.0]
XX= norms_dist_inv1D(XX_cpf)
Defined in
$HPEESOF_DIR/expressions/ael/statistical_fun.ael
See Also
norm_dist1D() (expmeas), norm_dist_inv1D() (expmeas), norms_dist1D() (expmeas),
lognorm_dist_inv1D() (expmeas), lognorm_dist1D() (expmeas), uniform_dist_inv1D()
(expmeas), uniform_dist1D() (expmeas)
pdf()
Returns a probability density function (PDF)
Syntax
y = pdf(data, numBins, minBin, maxBin)
Arguments
330
Measurement Expressions
Name
Description
Default
Range Type Required
data
the signal
None
(∞:∞)
Real Yes
numBins number of subintervals or bins used to
measure PDF
log(numOfPts)/log(2.0)
[1:∞)
Real No
minBin
beginning of the evaluation of the PDF
minimum value of the
data
(∞:∞)
Real No
maxBin
end of the evaluation of the PDF
maximum value of the
data
(∞:∞)
Real No
Examples
y = pdf(data)
y = pdf(data, 20)
Defined in
$HPEESOF_DIR/expressions/ael/statistical_fun.ael
See Also
cdf() (expmeas), histogram() (expmeas), yield_sens() (expmeas)
Notes/Equations
This function measures the probability density function of a signal. This function can only
be used by entering an equation (Eqn) in the Data Display window.
stddev()
This function calculates the standard deviation of the data
Syntax
y = stddev(data, flag)
Arguments
Name Description
Default Range Type
Required
data
data to find the stddev
None
Yes
flag
indicates how stddev normalizes 0
(∞:∞)
Real
[0:1] † Integer No
† When flag equals 0, the stddev normalizes by N-1, where N is the length of the data
sequence. Otherwise, stddev normalizes by N.
Examples
a = stddev(data)
a = stddev(data, 1)
331
Measurement Expressions
Defined in
$HPEESOF_DIR/expressions/ael/statistical_fun.ael
See Also
mean() (expmeas)
Notes/Equations
This function can only be used by entering an equation (Eqn) in the Data Display window.
stddev_outer()
Computes the stddev across the outer dimension of two-dimensional data
Syntax
y = stddev_outer(x, flag)
Arguments
Name Description
Default Range Type
Required
data
data to find the stddev
None
Yes
flag
indicates how stddev normalizes 0
(∞:∞)
Real
[0:1] † Integer No
† When flag equals 0, the stddev normalizes by N-1, where N is the length of the data
sequence. Otherwise, stddev normalizes by N.
Examples
a = stddev_outer(data)
a = stddev_outer(data, 1)
Defined In
$HPEESOF_DIR/expressions/ael/statistical_fun.ael
See Also
fun_2d_outer() (expmeas), max_outer() (expmeas), mean_outer() (expmeas),
min_outer() (expmeas)
Notes/Equations
The stddev_outer() function operates on the inner dimension of two-dimensional data.
332
Measurement Expressions
This function just calls the fun_2d_outer function, with stddev being the applied operation.
As an example, assume that a Monte Carlo simulation of an amplifier was run, with 151
random sets of parameter values, and that for each set the S-parameters were simulated
over 26 different frequency points. S21 becomes a [151 Monte Carlo iteration X 26
frequency] matrix, with the inner dimension being frequency, and the outer dimension
being Monte Carlo index. Now, assume that it is desired to know the stddev value of the
S-parameters at each frequency. Inserting an equation stddev(S21) computes the stddev
value of S21 at each Monte Carlo iteration. If S21 is simulated from 1 to 26 GHz, it
computes the stddev value over this frequency range, which usually is not very useful.
Inserting an equation stddev_outer(S21) computes the stddev value of S21 at each Monte
Carlo frequency.
uniform_dist1D()
Returns a uniform distribution: either its probability density function (pdf), or cumulative
distribution function (cdf)
Syntax
y = uniform_dist1D(data, A, B, is_cdf)
Arguments
Name Description
Default Range Type
data
number or a one-dimensional data
None
(-∞:∞) Integer, Real Yes
A
uniform distributed range
None
[0:∞)
Integer, real Yes
B
uniform distributed range
None
[0:∞)
Integer, real Yes
[0:∞)
†
Integer
is_cdf specifies cdf or pdf of standard uniform distribution 0
Required
No
† When is_cdf is not equal to "0", the function returns the cdf of the uniform distribution.
Otherwise, it returns the pdf of the uniform distribution.
Examples
X = 0.5
X_pdf= uniform_dist1D(X, 0.0,1.0, 0)
X_cdf = uniform_dist1D(X,0.0,1.0, 1)
XX=[-3.9::0.1::3.9]
XX_pdf = uniform_dist1D(XX,0.0,5.0,0)
XX_cdf = uniform_dist1D(XX,0.0,5.0,1)
Defined in
$HPEESOF_DIR/expressions/ael/statistical_fun.ael
See Also
norm_dist1D() (expmeas), norm_dist_inv1D() (expmeas), norms_dist_inv1D()
(expmeas), norms_dist1D() (expmeas), lognorm_dist_inv1D() (expmeas),
lognorm_dist1D() (expmeas), uniform_dist_inv1D() (expmeas)
333
uniform_dist_inv1D()
Measurement Expressions
Returns the inverse of the cumulative distribution function (cdf) for a uniform distribution
Syntax
y = uniform_dist_inv1D(data, A, B)
Arguments
Name Description
Default Range Type
Required
data
represents the cumulative probability None
[0:1]
Integer, Real Yes
A
uniform distributed range
None
[0:∞)
Integer, real Yes
B
uniform distributed range
None
[0:∞)
Integer, real Yes
Examples
X_cpf = 0.5
X= uniform_dist_inv1D(X_cpf, 0.0, 1.5)
XX_cpf=[0.0::0.01::1.0]
XX= uniform_dist_inv1D(XX_cpf, 0.0, 1.5)
Defined in
$HPEESOF_DIR/expressions/ael/statistical_fun.ael
See Also
norm_dist1D() (expmeas), norm_dist_inv1D() (expmeas), norms_dist_inv1D()
(expmeas), norms_dist1D() (expmeas), lognorm_dist_inv1D() (expmeas),
lognorm_dist1D() (expmeas), uniform_dist1D() (expmeas)
yield_sens()
Returns the yield as a function of a design variable
Syntax
y = yield_sens(pf_data, numBins)
Arguments
Name
Description
Default
Range Type
pf_data binary-valued scalar data set indicating the
pass/fail status of each value of a companion
independent variable
None
[0-1]
numBins number of subintervals or bins used to measure
yield_sens
log(numOfPts)/log(2.0) [1:∞)
Examples
a = yield_sens(pf_data)
a = yield_sens(pf_data, 20)
334
Required
Integer Yes
Real
No
Measurement Expressions
Defined in
$HPEESOF_DIR/expressions/ael/statistical_fun.ael
See Also
cdf() (expmeas), histogram() (expmeas), pdf() (expmeas)
Notes/Equations
Used in Monte Carlo simulation.
This function measures the yield as a function of a design variable. For more information
and an example refer to " Creating a Sensitivity Histogram " in the Optimization and
Statistical Design documentation.
This function can only be used by entering an equation (Eqn) in the Data Display window.
335
Measurement Expressions
Transient Analysis Functions
This section describes the transient analysis functions in detail. The functions are listed in
alphabetical order.
constellation() (expmeas)
cross() (expmeas)
fspot() (expmeas)
ifc tran() (expmeas)
ispec tran() (expmeas)
pfc tran() (expmeas)
pspec tran() (expmeas)
pt tran() (expmeas)
vfc tran() (expmeas)
vspec tran() (expmeas)
vt tran() (expmeas)
Working with Transient Data
Transient analysis produces real voltages and currents as a function of time. A single
analysis produces 1-dimensional data. Sections of time-domain waveforms can be indexed
by using a sequence within "[ ]".
constellation()
Generates the constellation diagram from Circuit Envelope, Transient, or Ptolemy
simulation I and Q data.
Syntax
Const = constellation(i_data, q_data, symbol_rate, delay)
Arguments
Name
Description
Default Range Type
i_data
in-phase component of data versus time of a single
complex voltage spectral component (for example, the
fundamental) †
None
(∞:∞)
Complex Yes
q_data
quadrature-phase component of data versus time of a
single complex voltage spectral component (for example,
the fundamental) †
None
(∞:∞)
Real
Yes
symbol_rate symbol rate of the modulation signal
None
[0:∞)
Real
Yes
delay
None
[0:∞)
Real
No
delay value † †
Required
† this could be a baseband signal instead, but in either case it must be real-valued versus
time.
† † (if nonzero) throws away the first delay = N seconds of data from the constellation
plot. It is also used to interpolate between simulation time points, which is necessary if
the optimal symbol-sampling instant is not exactly at a simulation time point. Usually this
parameter must be nonzero to generate a constellation diagram with the smallest
grouping of sample points.
Examples
336
Measurement Expressions
Rotation = -0.21
Vfund =vOut[1] * exp(j * Rotation)
delay =1/sym_rate[0, 0] - 0.5 * tstep[0, 0]
Vimag = imag(Vfund)
Vreal = real(Vfund)
Const = constellation(Vreal, Vimag, sym_rate[0, 0], delay)
where Rotation is a user-selectable parameter that rotates the constellation by
that many radians, and vOut is the named connection at a node. The parameter
delay can be a numeric value, or in this case an equation using sym_rate, the
symbol rate of the modulated signal, and tstep, the time step of the
simulation. If these equations are to be used in a Data Display window,
sym_rate and tstep must be defined by means of a variable (VAR) component, and
they must be passed into the dataset as follows: Make the parameter Other
visible on the Envelope simulation component, and edit it so that
Other = OutVar = sym_rate OutVar = tstep
In some cases, it may be necessary to experiment with the value of delay to get
the constellation diagram with the tightest points.
Note vOut is a named connection on the schematic. Assuming that a Circuit
Envelope simulation was run, vOut is output to the dataset as a two-dimensional
matrix. The first dimension is time, and there is a value for each time point
in the simulation. The second dimension is frequency, and there is a value for
each fundamental frequency, each harmonic, and each mixing term in the
analysis, as well as the baseband term.
vOut[1] is the equivalent of vOut[::, 1], and specifies all time points at the
lowest non-baseband frequency (the fundamental analysis frequency, unless a
multitone analysis has been run and there are mixing products). For former MDS
users, the notation "vOut[*, 2]" in MDS corresponds to the notation of
"vOut[1]".
Defined in
$HPEESOF_DIR/expressions/ael/digital_wireless_fun.ael
See Also
const_evm() (expmeas)
Notes/Equations
1. Used in Constellation diagram generation.
2. The I and Q data do not need to be baseband waveforms. For example, they could be
the in-phase (real or I) and quadrature-phase (imaginary or Q) part of a modulated
carrier. The user must supply the I and Q waveforms versus time, as well as the
symbol rate. A delay parameter is optional. The i_data and q_data must be of the
same dimension, and up to 5-dimensional data is supported.
3. The result of a constellation calculation using the constellation() function may be
plotted directly on a rectangular plot.
For example, you may add Const directly to a rectangular plot, where
337
Measurement Expressions
Const=constellation(Vreal,Vimag,sym_rate,delay).
If you want to plot Const on a polar plot, then add to the plot indep(Const)+j*Const.
cross()
Computes the zero crossings of a signal, interval between successive zero crossings or
slope at the crossing.
Syntax
yCross = cross(signal, direction, slope)
Arguments
Name
Description
Default
Range Type
Required
signal
the signal for which the zero crossing is to be found
None
(∞:∞)
Real
Yes
direction type of zero crossing †
0
[-1:1]
Integer Yes
slope
0 (no
slope)
[0:1]
Integer No
specifies if slope is to be calculated, rather than interval
between zero crossing
† If direction = +1, compute positive going zero crossings.
If direction = -1, compute negative going zero crossings.
If direction = 0, compute all zero crossings.
Examples
period=cross(vosc-2.0, 1)
This computes the period of each cycle of the vosc signal. The period is
measured from each positive-going transition through 2.0V.
period = cross(vosc-2.0, 1, 1) returns the zero crossings and the slope at the
zero crossings.
Defined In
Built in
Notes/Equations
The independent axis returns the time when the crossing occurred. If the third argument
is set to 1, the dependent axis returns the slope at zero crossing. Otherwise the
dependent axis returns the time interval since the last crossing (default behavior).
fspot()
Performs a single-frequency time-to-frequency transform
Syntax
y = fspot(x, fund, harm, windowType, windowConst, interpOrder, tstart)
Arguments
338
Measurement Expressions
Name
Description
Default
Range
Type
Required
x
time domain signal
None
(-∞:∞)
Real
Yes
fund
period 1/fund for the
Fourier transform
period that matches the length of
the independent axis of x
[1:∞)
Real
No
harm
harmonic number †
1
[1:∞)
Integer
No
windowType type of window to apply
to the data
0
[0:9] †† Integer,
String
No
windowConst window constant †† †
1
[0:∞)
No
interpOrder
interpolation scheme
None
[1:3] †† Integer
††
No
tstart
start time
1
[0:∞)
No
Real
Real
† harm=0 will compute the dc component of x.
†† The window types and their default constants are:
0 = None
1 = Hamming 0.54
2 = Hanning 0.50
3 = Gaussian 0.75
4 = Kaiser 7.865
5 = 8510 6.0
6 = Blackman
7 = Blackman-Harris
8 = 8510-Minimum 0
9 = 8510-Maximum 13
windowType can be specified either by the number or by the name.
†† † windowConst is not used if windowType is 8510
†† †† If the tranorder variable is not present, or if the user wishes to override the
interpolation scheme, then interpOrder may be set to a nonzero value:
1 = use only linear interpolation
2 = use quadratic interpolation
3 = use cubic polynomial interpolation
Examples
The following example equations assume that a transient simulation was
performed from 0 to 5 ns on a 1-GHz-plus-harmonics signal called vOut:
fspot(vOut)
returns the 200-MHz component, integrated from 0 to 5 ns.
fspot(vOut, , 5)
returns the 1-GHz component, integrated from 0 to 5 ns.
fspot(vOut, 1GHz, 1)
returns the 1-GHz component, integrated from 4 to 5 ns.
fspot(vOut, 0.5GHz, 2, , , , 2.5ns)
returns the 1-GHz component, integrated from 2.5 to 4.5 ns.
fspot(vOut, 0.25GHz, 4, "Kaiser")
returns the 1-GHz component, integrated from 1 to 5 ns, after applying the
default Kaiser window to this range of data.
fspot(vOut, 0.25GHz, 4, 3, 2.0)
returns the 1-GHz component, integrated from 1 to 5 ns, after applying a
Gaussian window with a constant of 2.0 to this range of data.
339
Measurement Expressions
Defined in
Built in
See Also
fft() (expmeas), fs() (expmeas)
Notes/Equations
fspot(x) returns the discrete Fourier transform of the vector x evaluated at one specific
frequency. The value returned is the peak component, and it is complex. The harmth
harmonic of the fundamental frequency fund is obtained from the vector x. The Fourier
transform is applied from time tstop-1/fund to tstop, where tstop is the last timepoint in x.
When x is a multidimensional vector, the transform is evaluated for each vector in the
specified dimension. For example, if x is a matrix, then fspot(x) applies the transform to
every row of the matrix. If x is three dimensional, then fspot(x) is applied in the lowest
dimension over the remaining two dimensions. The dimension over which to apply the
transform may be specified by dim; the default is the lowest dimension (dim=1). x must
be numeric. It will typically be data from a transient, signal processing, or envelope
analysis.
By default, the transform is performed at the end of the data from tstop-1/fund to tstop.
By using tstart, the transform can be started at some other point in the data. The
transform will then be performed from tstart to tstart+1/fund.
Unlike with fft() or fs(), the data to be transformed are not zero padded or resampled.
fspot() works directly on the data as specified, including non-uniformly sampled data from
a transient simulation.
Transient simulation uses a variable timestep and variable order algorithm. The user sets
an upper limit on the allowed timestep, but the simulator will control the timestep so the
local truncation error of the integration is controlled. If the Gear integration algorithm is
used, the order can also be changed during simulation. fspot() can use all of this
information when performing the Fourier transform. The time data are not resampled; the
Fourier integration is performed from timestep to timestep of the original data.
When the order varies, the Fourier integration will adjust the order of the polynomial it
uses to compute the shape of the data between timepoints.
This variable order integration depends on the presence of a special dependent variable,
tranorder, which is output by the transient simulator. If this variable is not present, or if
the user wishes to override the interpolation scheme, then interpOrder may be set to a
nonzero value.
Only polynomials of degree one to three are supported. The polynomial is fit because time
domain data are obtained by integrating forward from zero; previous data are used to
determine future data, but future data can never be used to modify past data.
ifc_tran()
340
Measurement Expressions
Returns frequency-selective current in Transient analysis
Syntax
y = ifc_tran(iOut, fundFreq, harmNum)
Arguments
Name
Description
Default Range Type
Required
iOut
current through a branch
None
(∞:∞)
Real, Complex Yes
fundFreq fundamental frequency
None
[0:∞)
Real
Yes
harmNum harmonic number of the fundamental
frequency
None
[0:∞)
Integer
Yes
Examples
y = ifc_tran(I_Probe1.i, 1GHz, 1)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
pfc_tran() (expmeas), vfc_tran() (expmeas)
Notes/Equations
This measurement gives RMS current, in current units, for a specified branch at a
particular frequency of interest. fundFreq determines the portion of the time-domain
waveform to be converted to the frequency domain. This is typically one full period
corresponding to the lowest frequency in the waveform. harmNum is the harmonic
number of the fundamental frequency at which the current is requested.
ispec_tran()
Returns current spectrum
Syntax
y = ispec_tran(iOut, fundFreq, numHarm, windowType, windowConst)
Arguments
341
Measurement Expressions
Name
Description
Default Range Type
Required
iOut
current through a branch
None
(∞:∞)
Real, Complex Yes
fundFreq
fundamental frequency
None
[0:∞)
Real
Yes
numHarm
number of harmonics of fundamental frequency None
[0:∞)
Integer
Yes
windowType type of window to be applied to the data
0
[0:9] † Integer, string No
windowConst window constant †† †
0
[0:∞)
Integer, Real
No
† The window types and their default constants are:
0 = None
1 = Hamming 0.54
2 = Hanning 0.50
3 = Gaussian 0.75
4 = Kaiser 7.865
5 = 8510 6.0 (This is equivalent to the time-to-frequency transformation with normalgate
shape setting in the 8510 series network analyzer.)
6 = Blackman
7 = Blackman-Harris
8 = 8510-Minimum 0
9 = 8510-Maximum 13
Examples
y = ispec_tran(I_Probe1.i, 1GHz, 8)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
pspec_tran() (expmeas), vspec_tran() (expmeas)
Notes/Equations
This measurement gives a current spectrum for a specified branch. The measurement
gives a set of RMS current values at each frequency. The fundFreq argument determines
the portion of the time-domain waveform to be converted to frequency domain. This is
typically one full period corresponding to the lowest frequency in the waveform. The
numHarm argument is the number of harmonics of fundamental frequency to be included
in the currents spectrum.
pfc_tran()
Returns frequency-selective power
Syntax
y = pfc_tran(vPlus, vMinus, iOut, fundFreq, harmNum)
342
Measurement Expressions
Arguments
Name
Description
Default Range Type
Required
vPlus
voltage at the positive terminal
None
(∞:∞)
Real,
Complex
Yes
vMinus
voltage at the negative terminal
None
(∞:∞)
Real,
Complex
Yes
iOut
current through a branch measured for power
calculation
None
(∞:∞)
Real,
Complex
Yes
fundFreq fundamental frequency
None
[0:∞)
Real
Yes
harmNum harmonic number of the fundamental frequency
None
[0:∞)
Integer
Yes
Examples
a = pfc_tran(v1, v2, I_Probe1.i, 1GHz, 1)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
ifc_tran() (expmeas), vfc_tran() (expmeas)
Notes/Equations
This measurement gives RMS power, delivered to any part of the circuit at a particular
frequency of interest. fundFreq determines the portion of the time-domain waveform to be
converted to frequency domain. This is typically one full period corresponding to the
lowest frequency in the waveform. harmNum is the harmonic number of the fundamental
frequency at which the power is requested.
pspec_tran()
Returns transient power spectrum
Syntax
y = pspec_tran(vPlus, vMinus, iOut, fundFreq, numHarm, windowType, windowConst)
Arguments
343
Measurement Expressions
Name
Description
Default Range Type
Required
vPlus
voltage at the positive terminal
None
(∞:∞)
Real,
Complex
Yes
vMinus
voltage at the negative terminal
None
(∞:∞)
Real,
Complex
Yes
iOut
current through a branch measured for power
calculation
None
(∞:∞)
Real,
Complex
Yes
fundFreq
fundamental frequency
None
[0:∞)
Real
Yes
numHarm
number of harmonics of fundamental frequency
None
[0:∞)
Integer
Yes
windowType type of window to be applied to the data
0
[0:9] † Integer,
string
windowConst window constant †† †
0
[0:∞)
No
Integer, Real No
† The window types and their default constants are:
0 = None
1 = Hamming 0.54
2 = Hanning 0.50
3 = Gaussian 0.75
4 = Kaiser 7.865
5 = 8510 6.0 (This is equivalent to the time-to-frequency transformation with normalgate
shape setting in the 8510 series network analyzer.)
6 = Blackman
7 = Blackman-Harris
8 = 8510-Minimum 0
9 = 8510-Maximum 13
Examples
a = pspec_tran(v1, v2, I_Probe1.i, 1GHz, 8)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
ispec_tran() (expmeas), vspec_tran() (expmeas)
Notes/Equations
This measurement gives a power spectrum, delivered to any part of the circuit. The
measurement gives a set of RMS power values at each frequency. The fundFreq argument
is the fundamental frequency that determines the portion of the time-domain waveform to
be converted to frequency domain (typically one full period corresponding to the lowest
frequency in the waveform). The numHarm argument is the number of harmonics of the
fundamental frequency to be included in the power spectrum.
pt_tran()
This measurement produces a transient time-domain power waveform for specified nodes.
344
Measurement Expressions
Syntax
y = pt_tran(vPlus, vMinus, current, fundFreq)
Arguments
Name
Description
vPlus
voltage at the positive terminal None
(∞:∞)
Real, Complex Yes
vMinus
voltage at the negative terminal None
(∞:∞)
Real, Complex Yes
current
current
None
(∞:∞)
Real, Complex Yes
None
[0:∞)
Real
fundFreq fundamental frequency
Default Range Type
Required
Yes
Examples
a = pt_tran(v1, v2, i1, 1GHz)
Defined In
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
vt() (expmeas), vt_tran() (expmeas)
Notes/Equations
DC-to-RF efficiency is based on HB analysis.
vfc_tran()
Returns the transient frequency-selective voltage
Syntax
y = vfc_tran(vPlus, vMinus, fundFreq, harmNum)
Arguments
Name
Description
Default Range Type
vPlus
voltage at the positive terminal
None
(∞:∞)
Real, Complex Yes
vMinus
voltage at the negative terminal
None
(∞:∞)
Real, Complex Yes
fundFreq fundamental frequency
None
[0:∞)
Real
Yes
harmNum harmonic number of the fundamental
frequency
None
[0:∞)
Integer
Yes
Examples
345
Required
Measurement Expressions
a = vfc_tran(vOut, 0, 1GHz, 1)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
ifc_tran() (expmeas), pfc_tran() (expmeas)
Notes/Equations
This measurement gives the RMS voltage across any two nodes at a particular frequency
of interest. The fundamental frequency determines the portion of the time-domain
waveform to be converted to frequency domain. This is typically one full period
corresponding to the lowest frequency in the waveform. The harmonic number is the
fundamental frequency at which the voltage is requested (positive integer value only).
vspec_tran()
Returns the transient voltage spectrum
Syntax
y = vspec_tran(vPlus, vMinus, fundFreq, numHarm, windowType, windowConst)
Arguments
Name
Description
Default Range Type
Required
vPlus
voltage at the positive terminal
None
(∞:∞)
Real, Complex Yes
vMinus
voltage at the negative terminal
None
(∞:∞)
Real, Complex Yes
fundFreq
fundamental frequency
None
[0:∞)
Real
Yes
numHarm
number of harmonics of fundamental frequency None
[0:∞)
Integer
Yes
windowType type of window to be applied to the data
0
[0:9] † Integer, string No
windowConst window constant
0
[0:∞)
Integer, Real
No
† The window types and their default constants are:
0 = None
1 = Hamming 0.54
2 = Hanning 0.50
3 = Gaussian 0.75
4 = Kaiser 7.865
5 = 8510 6.0 (This is equivalent to the time-to-frequency transformation with normalgate
shape setting in the 8510 series network analyzer.)
6 = Blackman
7 = Blackman-Harris
8 = 8510-Minimum 0
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Measurement Expressions
9 = 8510-Maximum 13
Examples
a = vspec_tran(v1, v2, 1GHz, 8)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
See Also
ispec_tran() (expmeas), pspec_tran() (expmeas)
Notes/Equations
This measurement gives a voltage spectrum across any two nodes. The measurement
gives a set of RMS voltages at each frequency. The fundamental frequency determines the
portion of the time-domain waveform to be converted to the frequency domain. This is
typically one full period corresponding to the lowest frequency in the waveform. The
numHarm argument is the number of harmonics of the fundamental frequency to be
included in the voltage spectrum.
vt_tran()
This measurement produces a transient time-domain voltage waveform for specified
nodes. vPlus and vMinus are the nodes across which the voltage is measured.
Syntax
y = vt_tran(vPlus, vMinus)
Arguments
Name Description
vPlus
Default Range Type
Required
voltage at the positive terminal None
(∞:∞)
Real, Complex Yes
vMinus voltage at the negative terminal None
(∞:∞)
Real, Complex Yes
Examples
a = vt_tran(v1, v2)
Defined in
$HPEESOF_DIR/expressions/ael/circuit_fun.ael
347
Measurement Expressions
See Also
vt() (expmeas)
348
Measurement Expressions
Utility Functions for Measurement Expressions
This section describes the utility functions in detail.
amodelb_snp() (expmeas)
design_name() (expmeas)
amodelb_snp()
Returns the cartesian difference between Two S Parameter matrices
Syntax
modelGoal = amodelb_snp( measured..S, model..S)
Arguments
Name Description
Default Range Type Required
Target the input S matrix that needs to be matched None
(∞:∞)
Real Yes
Model input S matrix to compare
(∞:∞)
Real Yes
None
Examples
modelGoal = abodelb_snp( measured..S, model..S)
design_name()
Returns design name given by TopDesignName in netlist.log
Syntax
design = design_name()
Arguments
Name Description Default Range Type Required
None
None
None
None
None No
Notes
The design_name() function returns the value of the TopDesignName parameter in the
netlist.log file. It allows the design name to be saved in the dataset for documentation.
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Measurement Expressions
Duplicated Expression Names
Expressions used in ADS are of three types:
Simulator Expressions (expsim) are used during a simulation; they are the
expressions that are added to a VAR block on a schematic page.
Measurement Expressions (expmeas) are used after a simulation, for post-processing
of simulation results. There are two ways to use them:
As MeasEqn blocks on a schematic page; although these blocks are on the
schematic, they execute only after the actual simulation has finished (except in
the case of Optimization; then the expression can be evaluated repeatedly, once
for each try). The MeasEqn result is also written to the dataset.
As EQN blocks on a DDS page; after the simulation has finished, these blocks
can be used to process the data for display or further calculations.
AEL Expressions (ael) are employed by users to develop custom functions. They can
be used wherever AEL is used. AEL expressions are valid even on a DDS page.
In many cases, the same function name is used for different types of expressions, and the
expressions can differ. For example, there is a step() Measurement Expression, a step()
Simulator Expression, and a step() AEL expression. Although these three expressions
operate similarly, the Simulator Expression assumes that the value passed in represents
time, and cannot be a complex number; that is not the case with the other two
expressions.
Because expressions with the same function name do not necessarily operate in the same
way, it is important to know which expression type will actually be used in a given
situation, and to be aware of any differences between that expression and others with the
same name.
Which Type is Used?
Where an expression name is duplicated, ADS uses the expression type that is appropriate
to the place in which the expression name appears:
Measurement expressions include all AEL expressions, plus some new functions that are
usable only in a measurement context and not in general AEL code. That is, AEL
Expression functions are a proper subset of Measurement Expression functions.
If the expression name appears in a VAR block on a schematic page, ADS interprets
it as a Simulator Expression. If no Simulator Expression is found by that name, an
Error is shown.
If the expression name appears in a MeasEqn block on a schematic page, ADS
interprets it as a Measurement Expression. If no Measurement Expression is found by
that name, but an AEL Expression is found, it is used, otherwise an Error is shown.
If the expression name appears in an EQN block on a DDS page, ADS interprets it as
a Measurement Expression. If no Measurement Expression is found by that name, but
an AEL Expression is found, it is used, otherwise an Error is shown.
If the expression name appears in an AEL file, ADS interprets it as an AEL
Expression. If no AEL Expression is found by that name, an Error is shown.
Expression Types and Expression Names
This table lists the duplicated expression names. Follow the links to find information about
350
the individual expressions.
Measurement Expressions
Measurement Expression
AEL Expression
Simulator Expression
abs() Measurement (expmeas)
abs() Function (ael)
abs() Expression (expsim)
acos() Measurement (expmeas)
acos() Function (ael)
acos() Expression (expsim)
acosh() Measurement (expmeas)
acosh() Function (ael)
acosh() Expression (expsim)
acot() Measurement (expmeas)
acot() Function (ael)
acoth() Measurement (expmeas)
acoth() Function (ael)
asin() Measurement (expmeas)
asin() Function (ael)
asinh() Measurement (expmeas)
asin() Expression (expsim)
asinh() Expression (expsim)
atan() Measurement (expmeas)
atan() Function (ael)
atan() Expression (expsim)
atan2() Measurement (expmeas)
atan2() Function (ael)
atan2() Expression (expsim)
atanh() Measurement (expmeas)
atanh() Function (ael)
atanh() Expression (expsim)
ceil() Measurement (expmeas)
ceil() Function (ael)
ceil() Expression (expsim)
chr() Measurement (expmeas)
chr() Function (ael)
cint() Measurement (expmeas)
cint() Function (ael)
cmplx() Measurement (expmeas)
cmplx() Function (ael)
complex() Measurement (expmeas)
complex() Expression (expsim)
conj() Measurement (expmeas)
conj() Function (ael)
convBin() Measurement (expmeas)
convBin() Function (ael)
conj() Expression (expsim)
convHex() Measurement (expmeas) convHex() Function (ael)
convOct() Measurement (expmeas)
convOct() Function (ael)
cos() Measurement (expmeas)
cos() Function (ael)
cos() Expression (expsim)
cosh() Measurement (expmeas)
cosh() Function (ael)
cosh() Expression (expsim)
cot() Measurement (expmeas)
cot() Function (ael)
cot() Expression (expsim)
coth() Measurement (expmeas)
coth() Function (ael)
coth() Expression (expsim)
db() Measurement (expmeas)
dB() Function (ael)
db() Expression (expsim)
dbm() Measurement (expmeas)
dBm() Function (ael)
dbm() Expression (expsim)
dbmtow() Measurement (expmeas)
dbmtow() Expression (expsim)
deg() Measurement (expmeas)
deg() Function (ael)
deg() Expression (expsim)
exp() Measurement (expmeas)
exp() Function (ael)
exp() Expression (expsim)
fix() Measurement (expmeas)
fix() Function (ael)
float() Measurement (expmeas)
float() Function (ael)
floor() Measurement (expmeas)
floor() Function (ael)
floor() Expression (expsim)
fmod() Measurement (expmeas)
fmod() Expression (expsim)
hypot() Measurement (expmeas)
hypot() Expression (expsim)
im() Measurement (expmeas)
im() Function (ael)
imag() Measurement (expmeas)
imag() Function (ael)
imag() Expression (expsim)
index() Function (ael)
index() Expression (expsim)
int() Function (ael)
int() Expression (expsim)
int() Measurement (expmeas)
jn() Measurement (expmeas)
jn() Expression (expsim)
list() Function (ael)
list() Expression (expsim)
ln() Measurement (expmeas)
ln() Function (ael)
ln() Expression (expsim)
log() Measurement (expmeas)
log() Function (ael)
log() Expression (expsim)
log10() Measurement (expmeas)
log10() Function (ael)
log10() Expression (expsim)
mag() Measurement (expmeas)
mag() Function (ael)
mag() Expression (expsim)
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Measurement Expressions
max2() Measurement (expmeas)
max2() Function (ael)
max() Measurement (expmeas)
max() Expression (expsim)
min() Measurement (expmeas)
min() Expression (expsim)
min2() Measurement (expmeas)
min2() Function (ael)
num() Measurement (expmeas)
num() Function (ael)
phase() Measurement (expmeas)
phase() Function (ael)
phasedeg() Measurement
(expmeas)
phasedeg() Function (ael) phasedeg() Expression
(expsim)
phase() Expression (expsim)
phaserad() Measurement (expmeas) phaserad() Function (ael) phaserad() Expression (expsim)
polar() Measurement (expmeas)
polar() Function (ael)
polar() Expression (expsim)
pow() Measurement (expmeas)
pow() Function (ael)
pow() Expression (expsim)
rad() Measurement (expmeas)
rad() Function (ael)
rad() Expression (expsim)
re() Measurement (expmeas)
re() Function (ael)
real() Measurement (expmeas)
real() Function (ael)
ripple() Measurement (expmeas)
real() Expression (expsim)
ripple() Expression (expsim)
round() Measurement (expmeas)
round() Function (ael)
sgn() Measurement (expmeas)
sgn() Function (ael)
sgn() Expression (expsim)
sin() Measurement (expmeas)
sin() Function (ael)
sin() Expression (expsim)
sinc() Measurement (expmeas)
sinc() Function (ael)
sinc() Expression (expsim)
sinh() Measurement (expmeas)
sinh() Function (ael)
sinh() Expression (expsim)
sprintf() Function (ael)
sprintf() Expression (expsim)
sqrt() Measurement (expmeas)
sqrt() Function (ael)
sqrt() Expression (expsim)
step() Measurement (expmeas)
step() Function (ael)
step() Expression (expsim)
strcat() Function (ael)
strcat() Expression (expsim)
sum() Measurement (expmeas)
sum() Expression (expsim)
tan() Measurement (expmeas)
tan() Function (ael)
tan() Expression (expsim)
tanh() Measurement (expmeas)
tanh() Function (ael)
tanh() Expression (expsim)
wtodbm() Measurement (expmeas)
xor() Measurement (expmeas)
wtodbm() Expression (expsim)
xor() Function (ael)
352